If a^2 + b^2 = 88 and ab = 6, (a > 0, b > 0) then what is the value of (a^3 + b^3) ?

Question 61

If $$a^2 + b^2 = 88 and ab = 6, (a > 0, b > 0)$$ then what is the value of $$(a^3 + b^3) ?$$

Solution

$$a^2 + b^2 = 88$$ and ab = 6,

$$(a + b)^2$$ - 2ab = 88

$$(a + b )^2$$ = 88 + 2*6

$$(a +b )^2$$ = 100

$$(a + b) $$ = 10(Square root of both sides)

therefore $$(a^3 + b^3) $$

$$(a + b)(a^2 - ab + b^2)$$

= 10*(88-6)

= 820

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