Question

On of x + y =a, x² + y2 = b then the value of x*3+y*3 is
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(A) ab (B) a² + b (C) a + b*3 (D)3ab -a*3 / 2
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Answer 1

Answer:

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ {a}^{2} = b + 2xy \\ \frac{ {a}^{2} - b}{2} = xy \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} + {y}^{2} - xy) \\ = (a)(b - \frac{ {a}^{2} - b }{2} ) \\ = (a)( \frac{2b - {a}^{2} + b}{2} \\ = \frac{3ab - {a}^{2} }{2}$