If a – b = 7 and a2 + b2 = 85, then find the value of a3 – b3.

If a – b = 7 and a² + b² = 85, then find the value of a³ – b³.

Answer :

We know that

(a – b)² = a² + b² – 2ab

Substituting the values

7² = 85 – 2ab

By further calculation

49 = 85 – 2ab

So we get

2ab = 85 – 49 = 36

Dividing by 2

ab = 36/2 = 18

Here

a³ – b³ = (a – b) (a² + b² + ab)

Substituting the values

a³ – b³ = 7 (85 + 18)

By further calculation

a³ – b³ = 7 × 103

So we get

a³ – b³ = 721

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