Question

যদি m+n=5 হয় এবং mn=6 হয় তবে (m2+n2)(m3+n3)=?​

Answer 1

$Given \: m + n = 5 \: --(1) \:and \\mn = 6 \: --(2)$

$i ) m^{2} + n^{2} \\= ( m + n )^{2} - 2 mn \\= 5^{2} - 2 \times 6 \\= 25 - 12 \\= 13 \: --(3)$

$ii ) m^{3} + n^{3} \\= ( m + n )^{3} - 3mn ( m + n ) \\= 5^{3} - 3 \times 6 \times 5 \\= 125 - 90 \\= 35 \:--(4)$

$Now , \red{ Value \:of \: (m^{2} + n^{2} )( m^{3} + n^{3} ) } \\= 13 \times 35 \\= 455$

Therefore.,

$\red{ Value \:of \: (m^{2} + n^{2} )( m^{3} + n^{3} ) } \green {= 455 }$

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Answer 2

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