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If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2?

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If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2?  [#permalink]

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New post 18 Jan 2016, 22:43
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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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Posts: 6961
Re: If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2?  [#permalink]

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New post 18 Jan 2016, 23:04
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fattty 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


Hi,
I have formatted your Q. It would be helpful to you if you read how to write mathematical formulas given write above the text box.

now for the Q..
Whenever we see x+y, xy and x^2+y^2 together, it makes sense to employ (x+y)^2...

now given
If x + y = 6t..
square both sides..
\((x+y)^2=36t^2\)..
\(x^2+y^2+2xy=36t^2\)..(i)
also given
\(xy = -7t^2\)..
multiply both sides by 2..
\(2xy = -14t^2\)..
subtract this from (i)
\(x^2+y^2+2xy-2xy=36t^2-(-14t^2)\)..
\(x^2+y^2=50t^2\)..

so
\(\frac{(x^2 + y^2)}{t^2}\)=\(50t^2/t^2=50\)
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Re: If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2?  [#permalink]

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New post 09 Mar 2017, 00:41
x^2 + y^2 = (x+y)^2 - 2xy = (6t)^2 - 2 (-7t^2) = 50 t^2

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

Option C

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