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

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Intern
Joined: 29 Nov 2015
Posts: 11
If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2?  [#permalink]

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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
Math Expert
Joined: 02 Aug 2009
Posts: 6961
Re: If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2?  [#permalink]

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18 Jan 2016, 23:04
1
1
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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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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Re: If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2? &nbs [#permalink] 09 Mar 2017, 00:41
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# If x + y = 6t and xy = -7t2,what is the value of (x2 + y2)/t2?

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