Question

If a+b = 8 and
${a}^{2} + {b}^{2} = 10$
find the value of
${a}^{3} + {b}^{3}$

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Answer 1

${a}^{3} + {b}^{3} = {(a + b)}^{3} - 3ab(a + b) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {8}^{3} - 3ab(8) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 512 - 24ab \\ \\ {(a+b)}^2 ={a}^2+{b}^2+2ab\\ \\ \: \: \: \: {8}^2=\:10+2ab \\ \\ \: \: \: ab =27 \\ \\ {a}^3+{b}^3=512- 648=-136\\ \\ hope \: it \: helps \: you$

Answer 2

Answer will b -136.

Hope it helps u!!...