a+b=10,a square+b square =58. Find a cube+b cube

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Solution

Given,

a +b = 10

a² + b² = 58

We know that,

(a+b)² = a² +b² +2ab

10² = 58 +2ab

100 = 58 + 2ab

2ab = 42
ab = 21

Again,

(a+b)³ = a³ +b³ + 3ab(a+b)

10³ = a³ +b³ + 3*21(10)

10³ = a³ + b³ +630

1000 - 630 = a³ +b³

a³ + b³ = 370

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