Question

M+n=5 mn=6 (m2+n2)(m3+n3)=

Answer 1

$given \: \: \: \: \: m + n =5 \\ \: \: \: \: \: \: \: \: mn = 6 \\ \\ {m}^{2} + {n}^{2} = ( {m + n})^{2} - 2mn \\ = {5}^{2} - 2 \times 6 \\ = 25 - 12 \\ = 13 \\ \\ {m}^{3} + {n}^{3} = ( {m + n})^{3} - 3mn(m + n) \\ = {5}^{3} - 3 \times 6 \times 5 \\ = 125 - 90 \\ = 35 \\ \\ ( {m}^{2} + {n}^{2} )( {m}^{3} + {n}^{3} ) = 13 \times 35 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 455$