Question

if a + b = 12 and a² + b² = 58. find a³ +b³​

Answer 1

Answer:

a + b = 12

On squaring both sides-

(a + b)² = (12)²

a² + b² + 2ab = 144

58 + 2ab = 144

2ab = 144 - 58

2ab = 86

ab = 86/2

ab = 43

Now, we know that-

a³ + b³ = (a + b)(a² + b² - ab)

⇒ a³ + b³ = 12 ( 58 - 43 )

⇒ a³ + b³ = 12 * 15

⇒ a³ + b³ = 180

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Answer 2

a3+b3=(a+b)3-3ab+(a+b)

(a+b)(a2+b2)=(10)3-3ab+(10)

(10)(58)=1000-3ab+10

580=1010-3ab

3ab=1010-580

ab=430/3

ab=143.3