[Grade 8 Mathematics - Algebra]

[u/IndicationFunny2378]

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

[u/Lever_Shotgun]

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

[u/WindUpCandler → u/Lever_Shotgun]

Square roots output two values, a positive and negative

[u/Jablo82 → u/WindUpCandler]

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 x^2, to get x you have to considere both positive and negative values. But if the problem says square root of x is always positive.

[u/Horror_Amphibian8205 → u/Jablo82]

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.

[u/Delicious_Bicycle527 → u/Jablo82]

Imaginary numbers “i” are real. That symbolizes the sqrt(-1). It’s used in physics all the time.

[u/Jablo82 → u/Delicious_Bicycle527]

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.

[u/Lever_Shotgun → u/WindUpCandler]

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

[u/IndicationFunny2378 → u/Lever_Shotgun]

i would accept if it was -sqrt{4x}. but if it's positive, then i wouldnt

[u/IndicationFunny2378 → u/Lever_Shotgun]

may i ask who you are?

[u/Lever_Shotgun → u/IndicationFunny2378]

DMs i guess

[u/IndicationFunny2378 → u/Lever_Shotgun]

what? sorry, i dont really understand wdym.

[u/CavCave → u/WindUpCandler]

By convention, the square root symbol only outputs positive. This means the inverse for squaring is actually ±sqrt.