If x \neq 0 and x = 4xy - 4y^2, then in terms of y, x = ?

Free Practice Question

PS · Problem Solving

605-655

Exponents/Powers

If $x \neq 0$ and $x = \sqrt{4xy - 4y^2}$ , then in terms of $y$ , $x =$ ?

Answer Choices

Correct answer marked below

2y

Correct

y

y^2

\frac{4y^2}{1-4y}

-2y

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Comments

DhruvAug 5

Thanks, I initially tried squaring both sides but got tangled up. The answer choices helped me see it was a perfect square.

KevinAug 9

Same here! I was stuck until I recognized the quadratic form.

GuruprasadMay 27

Wait, how do we know x is positive? The square root is nonnegative, but x could be negative if the inside is zero... but x ≠ 0. So doesn't that force x positive?

AsiaJun 6

Good point, since sqrt is never negative and x ≠ 0, x must be > 0. That's crucial.

IoannisJul 13

This was a bit tricky with the algebra. I got y = x/2 after simplifying, but had to double-check because the choices have both 2y and y.

SukanayaJul 14

I think you might have flipped it? Let me redo: squaring gives x^2 = 4xy - 4y^2, then rearrange to x^2 - 4xy + 4y^2 = 0, which is (x - 2y)^2 = 0, so x = 2y.

AniketJul 17

Nice problem! The perfect square trinomial was a neat twist. Difficulty felt around 650.

What this question tests

What it tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Common trap

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).

If x≠0x \neq 0x=0 and x=4xy−4y2x = \sqrt{4xy - 4y^2}x=4xy−4y2​, then in terms of yyy, x=x =x= ?