Question

If $x^a\cdot x^b\cdot x^c=1(x\ne 0),$ the value of $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$ is

• A. $0$
• B. $abc$
• C. $3abc$
• D. $3$

Answer 1

The correct option is A $0$

$x^a\cdot x^b\cdot x^c=1$

$x^{(a+b+c)}=1$

$a+b+c=0$

Now $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}=\frac{a^3+b^3+c^3}{abc}=\frac{(a+b+c)(a^2+b^2+c^2-ab-bc-ca)}{abc}=\frac{0(a^2+b^2+c^2-ab-bc-ca)}{abc}=0$

Hence the correct option is (A).