If y + 1y = 4, what is y^2 + 1y^2? | GMAT Sprint

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PS · Problem Solving

sub-505

Algebra

If $y + \frac{1}{y} = 4$ , what is $y^2 +\frac{1}{y^2}$ ?

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Explanation

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Official Explanation

Official

To find

y^2 +\frac{1}{y^2}

, we can use the identity:

y^2 +\frac{1}{y^2} = ( y + 1/y )^2 - 2

. Given that

y + 1/y = 4

, we first calculate

(y +\frac{1}{y})^2

:…

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Comments

PriteshApr 6, 2025

greatt question!

AnuragApr 5, 2025

thanks

SiddhiApr 27, 2025

Thank for sharing!!!

ShubhankarMar 2, 2025

This is definitely a test-day trap

UdayAug 3, 2024

greatt question!

NayanApr 6, 2024

Thank you very much!

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

If y+1y=4y + \frac{1}{y} = 4y+y1​=4, what is y2+1y2y^2 +\frac{1}{y^2}y2+y21​?