Question

If a+b=8, ab=15 and a²+b²=34 then find the value of a³+b³

Answer 1

We know that,
(a+b)³ = a³ + b³ + 3ab (a+b)

$\green{GIVEN :- }$
(a+b) = 8
ab = 15
a² + b² = 34

(a+b)³ = a³ + b³ + 3ab (a+b)

➡ (8)³ = a³ + b³ + 3*15 (8)

➡ 512 = a³ + b³ + 360

➡ 512-360 = a³ + b³

➡ 152 = a³ + b³

$\red {152}$ = $\blue{a}$³ + $\pink{b}$³

Answer 2

Given

a+b = 8

ab = 15

a^2 +b^2 = 34

we know that (a+b)^3 = a^3 +b^3 +3ab(a+b)

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

(8)^3 - 3(15)(8) = a^3 + b^3

512 - 360 = a^3 + b^3

152 = a^3 +b^3