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Bunuel
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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Bunuel
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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