Question 74

If a + b = 5 and ab = 3, then $$(a^3 + b^3)$$ is equal to:

Solution

Given that $$a+b=5$$ and $$ab=3$$

We know that, $$(a+b)^3=a^3+b^3+3ab(a+b)$$

$$\Rightarrow a^3+b^3=(a+b)^3-3ab(a+b)-----------(i)$$

Now, substituting the values in the equation (i)

So, $$\Rightarrow a^3+b^3=(5)^3-3\times 3(5)$$

$$\Rightarrow a^3+b^3=125-45$$

$$\Rightarrow a^3+b^3=80$$

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