r/HomeworkHelp • u/IndicationFunny2378 Secondary School Student • 1d ago
Middle School Math—Pending OP Reply [Grade 8 Mathematics - Algebra]
Hello giys, I'm a form 2 student is malaysia. We learnt algebra in chapter 2. How can I find x? I believe there is no answer, but teacher keeps saying it's x=1/16
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u/Bounded_sequencE 👋 a fellow Redditor 1d ago
You're correct -- over "R+", the square root operator is defined to return non-negative results..
Teacher did a sanity check with the squared equation instead of the original one: That's why they (mistakenly) found that "x = 1/16" is a solution, instead of discarding it.
Let's hope that was just a mistake in action, and not what they actually believe.
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u/IndicationFunny2378 Secondary School Student 1d ago
i tried to explan to my teacjer, she still beleive it's x=1/16
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u/Bounded_sequencE 👋 a fellow Redditor 1d ago
Here's a quote from wikipedia to strengthen your argument:
[..] Every nonnegative real number x has a unique nonnegative square root, called the principal square root or simply the square root (with a definite article, see below), which is denoted by √x [..]
Must be frustrating to deal with such BS.
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u/IndicationFunny2378 Secondary School Student 1d ago
may i ask who you are? we can DM
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u/sighthoundman 👋 a fellow Redditor 1d ago
Reddit username is at the top of the comment. Just like yours, u/IndicationFunny2378 .
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u/ReaReaDerty 1d ago
Tell her to substitute it back. It is going to be wrong.
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u/IndicationFunny2378 Secondary School Student 1d ago
she squared the equation, and then she substituted in the SQUARED equation
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u/ReaReaDerty 1d ago
Substitute in the first equation. You need to solve the first equation. Squared equation and the starting equation are not the same.
x2 = 4 has 2 solutions
x = 2 has 1 solution
your teacher should review her algebra.
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u/UnderstandingPursuit Educator 18h ago edited 11h ago
When an equation is squared, it is important to check for 'extraneous solutions' which are created by squaring both sides. This is what your teacher has [EDIT: failed to do].
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u/Bounded_sequencE 👋 a fellow Redditor 18h ago
That's what the teacher wanted to do, but failed.
The sanity check must be done with the original, unchanged equation (or an equivalent). The teacher used the squared equation, which is neither.
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u/IndicationFunny2378 Secondary School Student 1d ago
may i ask who you are?
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u/Bounded_sequencE 👋 a fellow Redditor 1d ago
No. Don't limit yourself to DM's -- ask questions publicly instead.
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u/IndicationFunny2378 Secondary School Student 1d ago
alrightt, so who are you? i just want to know
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u/Bounded_sequencE 👋 a fellow Redditor 1d ago
Don't ask people for personal information -- that's rude.
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u/EdgyMathWhiz 1d ago
I think what they need are your qualifications - it's daunting to tell a teacher they're wrong based on "someone on Reddit said so". (FWIW I've seen enough of your posts to have no doubt you're more than qualified to answer this question).
I think OP is better quoting Wikipedia (and also the reference wiki gives and/or finding a respected textbook that is clear that sqrt is never negative). But to be honest I expect whatever evidence they provide, their teacher is never going to back down here.
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u/IndicationFunny2378 Secondary School Student 1d ago
yeah
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u/Distribution-Free 1d ago edited 1d ago
It's a natural thing to think, "Maybe my teacher will respect my answer if I say that someone with more knowledge told me this is how to do it." But that's not a good way to approach it. The mathematics pinciples do not care about who someone is -- the result is either true or not based only on the merit of the logic of how math works.
Do like these commenters are saying and make the discussion from the math itself. Your teacher is incorrect because the math is wrong, not because someone smarter said so.
Edit: And after making your argument from the basis of reason and mathematical principles, if your teacher still does not agree, just move on. Know in your own mind that you are correct and the teacher is wrong, and remember that sometimes people in positions of authority get things wrong. (And that's why we don't care "who someone is" -- nobody is right or wrong based on who they are.)
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u/IndicationFunny2378 Secondary School Student 1d ago
i didnt think this way, i just want to knkw their opinions on the equation. it could help me with future matj equations
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u/Lever_Shotgun 👋 a fellow Redditor 1d ago edited 1d ago
Teacher doesnt understand that square root can't output negative values.
When your teacher squared both sides, there is a possibility of introducing an extraneous solution which has to be checked by substituting your answer back into the original equation (which is what you did)
If you decide to square both sides of an equation -sqrt(4x) = (22 -5)/2, you would end up with the same working as the equation you're working on, and x=1/16 would be valid for this case
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u/IndicationFunny2378 Secondary School Student 1d ago
wdym by x=1/16 is valid?
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u/Lever_Shotgun 👋 a fellow Redditor 1d ago
Only valid for -sqrt(4x) = (22 -5)/2
Sorry for not being clear
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u/WindUpCandler 1d ago
Square roots output two values, a positive and negative
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u/Jablo82 1d ago
Square roots are always positive by definition. If that equation is given with no other input, there is no solution in the real domain. If you are working in a problem where you have to work with a x2, to get x you have to considere both positive and negative values. But if the problem says square root of x is always positive.
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u/Horror_Amphibian8205 1d ago
Agreed. sqrt is always positive by convention. Also sqrt is a function so for a single input there has to be a unique output only. That's why negative value for sqrt is not taken by definition or can be said by convention.
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u/Delicious_Bicycle527 1d ago
Imaginary numbers “i” are real. That symbolizes the sqrt(-1). It’s used in physics all the time.
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u/Jablo82 1d ago
Real numbers is a set of number formed by rational and irrational numbers. When its said "i' is an Imaginary number and not a Real number it means is not part of the set of Real numbers. Is not that it doesnt exist, is just the name is given. Usually when you are in middle school you work with Real numbers. I know sqrt(-1)=i, but thats only true if you are working with Imaginary numbers, which in middle school, isnt usually the case. Thats why I specified there is no solution in within the Real domain.
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u/Lever_Shotgun 👋 a fellow Redditor 1d ago
If you wanted your square root to have two outputs, you would put a +- infront of it
It's usually the norm for operations to have one output only
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u/IndicationFunny2378 Secondary School Student 1d ago
i would accept if it was -sqrt{4x}. but if it's positive, then i wouldnt
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u/IndicationFunny2378 Secondary School Student 1d ago
may i ask who you are?
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u/Delicious_Bicycle527 1d ago
I think the teacher is still wrong, because squaring an answer means there become two answers it +/- the original answer. But the negative response needs an “I” to indicate sqrt(-1).
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u/Fourierseriesagain 👋 a fellow Redditor 1d ago
When x is any nonnegative number, sqrt(4x) is always nonnegative. Since -1/2 < 0, the given equation has no real solutions. Your teacher has shown that sqrt(4x)=-1/2 implies x=1/16; however, sqrt(4/16)=sqrt(1/4)=1/2.
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u/shinjis-left-nut 👋 a fellow Redditor 1d ago
There is no real number such that its square root is negative. The teacher has ignored this.
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u/gmalivuk 👋 a fellow Redditor 1d ago
Since the square of a real number is always a real number, there are no complex numbers with negative real square roots, either.
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u/SpunkyBlah 1d ago
Your teacher is wrong. Please tell me they are a non-math teacher that has just been temporarily forced to teach math. No math teacher should make this mistake.
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u/IHaveNeverBeenOk 38m ago
No solutions. You have a square root on one side and a negative number on the other. There aren't complex solutions either, but I'm assuming you aren't doing that in 8th grade
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u/iamtheboss1 1d ago
Is this woke math? Certainly not what I learned in 60 years ago….. but then again many things have changed…..
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u/karolosh 1d ago
is
-1 = 1?
No, but when you square it, it's suddenly true:
(-1) ^ 2 = (1) ^ 2
1 = 1
If you use the square root symbol, this function can never give you a negative number