Question

if m+n=5 and mn=6 then find (m²+n²)(m³+n³)

​

Answer 1

(m+n)²=m²+n²+2mn

m²+n²= (m+n)²-2mn

=5² - 2(6)

= 25 - 12

m²+n²= 13

(m+n)³=m³+n³+3mn(m+n)

m³+n³= (m+n)³-3mn(m+n)

= 5³-3(6)(5)

= 125 - 90

m³+n³= 35

(m²+n²)(m³+n³) = 13×35

=455

Hope it helps you

mark as brainliest

Answer 2

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