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

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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!

AbrahamSep 19

thanks, this was a nice quick one. squaring the whole thing basically gives it to you

ZofishanSep 24

wait can you explain why we square? i get lost on the middle term

TanveerAug 24

got 14, pretty fast for a sub-505. just remember the little +2 hiding in there

SahilSep 2

this is the exact trap i fell into lol. forgot to subtract the 2 and picked C

DivyanshSep 21

is the trick basically the same pattern for any y + 1/y question? like if it were 5 instead of 4 would i do the same squaring move?

RishabhSep 25

yep same idea every time, square both sides and watch the constant term

RitikaSep 22

difficulty felt right. straightforward once you spot that you just square the given expression.

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​?