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If 3x + 5y = 11 and xy = 2, find the value of 9x^2 + 25y^2

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 If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2

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We know that 3x + 5y = 11 and xy = 2

Upon squaring on both sides of the given expression, we get

(3x + 5y)2 = 112

(3x)2 + (5y)2 + 2(3x)(5y) = 121

9x2 + 5y2 + 2 (15xy) = 121   (since xy=2)

9x2 + 5y2 + 2(15(2)) = 121

9x2 + 5y2 + 60 = 121

9x2 + 5y2 = 121-60

9x2 + 5y2 = 61

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