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

\(\frac{(x^2 + y^2)}{t^2}\)=\(50t^2/t^2=50\)

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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