Question

if a+b=8 and ab=6, find the values of a^3+b^3.

Answer 1

a^3 +b^3 = (a + b)(a^2+b^2 - ab)

= 8( a^2 +b^2 - 6)

Now a^2 +b^2 = (a+ b)^2 - 2ab

a^2 + b^2 = (8)^2 - 2×6 = 64 - 12 = 52

= 8(52 - 6)

= 8 × 46

= 368


Thanks

Answer 2

$hey \\ here \: is \: your \: answer \\ \\ (a + b) ^{ 3} = a ^{3} + b {}^{3} + 3ab \: (a + b ) \\ \\ (8) {}^{3} = a {}^{3} + b {}^{3} + 3 \times 6(8) \\ \\ \\ 512 = a {}^{ 3} + b {}^{3} + 144 \\ \\ answer \: 512 - 144 = 368$

hope it helps