If a + b = 5 and ab = 3, then $$(a^3 + b^3)$$ is equal to:
Given that,
$$a+b=5$$ and $$ab=3$$
Now, $$a+b=5$$
squaring both side,
$$\Rightarrow(a+b)^2=25$$
$$\Rightarrow(a+b)^2=a^2+b^2+2ab$$
$$\Rightarrow(a+b)^2=a^2+b^2+2ab$$
$$\Rightarrowa^2+b^2=25-2ab=$$
$$\Rightarrowa^2+b^2=25-2\times3=19$$
$$\Rightarrow(a^3 + b^3)=(a+b)(a^2+b^2-ab)$$
$$\Rightarrow(a^3 + b^3)=(5)(19-3)$$
$$\Rightarrow(a^3 + b^3)=80$$
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