Question

if x+y = 5 and xy= 6 then x^3+y^3 = ?​

Answer 1

Answer:

$x {}^{3} + y {}^{3} = (x + y) {}^{3} - 3(xy)(x + y)$

$(5) {}^{3} - 3(6)(5)$

125-90

35

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Answer 2

$\huge \mathcal \blue{AnswEr : - }$

$\bf \: x + y = 5........(1) \\ \\ \bf \: xy = 6......(2) \\ \\ from \: eq(1) \\ \\ \bf \: y = 5 - x......(3) \\ \\ \sf \: \: substitute \: \: eq(3) \: \: in \: \: eq(2) \\ \\ \bf \implies \: x(5 - x) = 6 \\ \\ \bf \implies \: 5x - {x}^{2} = 6 \\ \\ \bf \implies \: {x}^{2} - 5x + 6 = 0 \\ \\ \bf \implies \: {x}^{2} - 2x - 3x + 6 = 0 \\ \\ \bf \implies \: x(x - 2) - 3(x - 2) = 0 \\ \\ \bf \implies \: ( x- 2)(x - 3) = 0 \\ \\ \bf \implies \: x = 3 \\ \\ \bf \implies \: y = 5 - 3 = 2 \\ \\ now \\ \\ \bf \implies \: {x}^{3} + {y}^{3} = {(3)}^{3} + {(2)}^{3} = 27 + 8 = 35$