If $$a + b = 27$$ and $$a^3 + b^3 = 5427$$, then find $$ab$$.
Given, Â $$a + b = 27$$
$$a^3 + b^3 = 5427$$
$$=$$> Â $$\left(a+b\right)\left(a^2+b^2-ab\right)=5427$$
$$=$$> Â $$27\left(a^2+b^2+2ab-3ab\right)=5427$$
$$=$$> Â $$\left(a+b\right)^2-3ab=201$$
$$=$$> Â $$\left(27\right)^2-3ab=201$$
$$=$$> Â $$729-3ab=201$$
$$=$$> Â $$3ab=729-201$$
$$=$$> Â $$3ab=528$$
$$=$$> Â $$ab=176$$
Hence, the correct answer is Option C
Create a FREE account and get:
