Question

if a-b=7and a2+b2=85then find the value of a3-b3​

Answer 1

Answer: 721

Step-by-step explanation:

Given:

$(a-b) = 7; a^2 + b^2 = 85$

We know that:

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

Also,

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

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

$85 - (7)^2 = 2ab$

$85-49 = 2ab$

=> $ab = \frac{36}{2} = 18$

∴ $a^3- b^3 = (a-b)(a^2+b^2 + ab)$

=> $a^3-b^3 = (7)(85+18)$

=> $a^3 - b^3 = 7*103$

=> $a^3 - b^3 = 721$

Answer: $a^3 - b^3 = 721$

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