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