Given, $a + b = 10, a^{2} + b^{2} = 58$ , then find $a^{3} + b^{3} =$

340

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370

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390

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410

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Solution

The correct option is B $370$
Given a+b =10
so $(a + b)^{2} = a^{2} + b^{2} + 2 a b 10^{2} = 58 + 2 a b ∴ 2 a b = 100 - 58 = 42 ∴ a b = 21 (a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b) 10^{3} = a^{3} + b^{3} + 3 \times 21 \times 10 ∴ a^{3} + b^{3} = 1000 - 630 = 370$

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