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If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2?

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Bunuel
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If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2? [#permalink] New post  13 Feb 2020, 07:50
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If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?

A. 20
B. 30
C. 50
D. 60
E. 90
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BrentGMATPrepNow
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Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2? [#permalink] New post  13 Feb 2020, 08:13
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Bunuel wrote:
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of \(\frac{(x^2 + y^2)}{t^2}\)?

A. 20
B. 30
C. 50
D. 60
E. 90


Given: \(x + y = 6t\)
Square both sides to get: \((x + y)^2 = (6t)^2\)
Expand and simplify: \(x^2 + 2xy + y^2 = 36t^2\)

Also given: \(xy = -7t^2\)
Multiply both sides by 2 to get: \(2xy = -14t^2\)

We now have two equations:
\(x^2 + 2xy + y^2 = 36t^2\)
\(2xy = -14t^2\)

Subtract the bottom equation from the top equation to get: \(x^2 + y^2 = 50t^2\)

Our goal is to find the value of \(\frac{(x^2 + y^2)}{t^2}\)

Replace the numerator with its equivalent value to get: \(\frac{50t^2}{t^2}\)

Simplify to get: 50

Answer: C

Cheers,
Brent
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Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2? [#permalink] New post  14 Feb 2020, 08:13
given
\(\frac{(x^2 + y^2)}{t^2}\)
can be re written as ;
\(\frac{(x^2 + y^2+2xy-2xy)}{t^2}\)
\(\frac{(x + y)^2-2xy}{t^2}\)
substitute given function values
we get 50 as answer
IMO C


Bunuel wrote:
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?

A. 20
B. 30
C. 50
D. 60
E. 90
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ScottTargetTestPrep
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Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 17428
Location: United States (CA)
Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2? [#permalink] New post  21 Feb 2020, 09:03
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Bunuel wrote:
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?

A. 20
B. 30
C. 50
D. 60
E. 90


Squaring the first equation, we have:

x^2 + y^2 + 2xy = 36t^2

Substituting -7t^2 for xy, we have:

x^2 + y^2 - 14t^2 = 36t^2

x^2 + y^2 = 50t^2

So, we have:

(x^2 + y^2) / t^2 = 50t^2 / t^2 = 50

Answer: C
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Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2? [#permalink] New post  05 Aug 2020, 00:01
Bunuel wrote:
If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?

A. 20
B. 30
C. 50
D. 60
E. 90


Asked: If \(x + y = 6t\) and \(xy = -7t^2\),what is the value of\(\frac{(x^2 + y^2)}{t^2}\)?

\(x^2 + y^2 = (x+y)^2 - 2xy = 36t^2 + 14t^2 = 50t^2\)

\(\frac{(x^2 + y^2)}{t^2} = 36\)

IMO C
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Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2? [#permalink] New post  06 Nov 2022, 16:07
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Re: If x + y = 6t and xy = -7t^2,what is the value of (x^2 + y^2)/t2? [#permalink]
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