Question

if m+n=5and mn=6 then (m²+n²) (m³+n³)

Answer 1

m+n=5
Squaring both the sides
m²+n²+2mn=25
m²+n²+12=25
m²+n²=13
Now m³+n³=(m+n) (m²+n²-mn)
=5(13-6)
=35
Hence m²+n²) (m³+n³) =13(35)
=455

Answer 2

m + n = 5
Squaring on both the sides !!!
(m + n)^2 = 25
25= m^2 + 2mn + n^2
25 = m^2 + n^2 + 2(6)
m^2 + n^2 = 25 - 12
m^2 + n^2 = 13

now
m^3 + n^3 = (m+n)(m^2 - mn + n^2)
m^3 + n^3 = 5 ( 13 - 6 )
= 5 × 7
=35

therefore;

$({m}^{2} + {n}^{2} )({m}^{3} + {n}^{3} )$
13×35 = 455