Question

If a+b=10 and a^2+b^2=58,find the value of a^3+b^3

Answer 1

a + b = 10

a² + b² = 58

________________ [GIVEN]

• We have to find the value of a³ + b³.

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a + b = 10

Squaring on both sides

$\implies$ (a + b)² = (10)²

$\implies$ a² + b² + 2ab = 100

$\implies$ 58 + 2ab = 100

$\implies$ 2ab = 100 - 58

$\implies$ 2ab = 42

$\implies$ ab = 21

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a + b = 10

Take cube on both sides

$\implies$ (a + b)³ = (10)³

$\implies$ a³ + b³ + 3ab (a + b) = 1000

$\implies$ a³ + b³ + 3(21) (10) = 1000

$\implies$ a³ + b³ + 630 = 1000

$\implies$ a³ + b³ = 1000 - 630

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a³ + b³ = 370

_____________ [ANSWER]

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Answer 2

To find : value of a³ + b³

a + b = 10

Squaring on both sides,

(a + b)² = (10)²

a² + b² + 2ab = 100

58 + 2ab = 100

2ab = 100 - 58

ab = 21

Now,

a + b = 10

Cubing on both sides

(a + b)³ = (10)³

a³ + b³ + 3ab (a + b) = 1000

a³ + b³ + 3 × (21) (10) = 1000

a³ + b³ + 630 = 1000

a³ + b³ = 370

Answer : 370