Question

If a, b, c are in G.P, then

• A. $a(b^2+c^2)=c(b^2+c^2)$
• B. $a(b^2+c^2)=c(a^2+b^2)$
• C. $a^2(b+c)=c^2(a+b)$
• D. none of these

Answer 1

The correct option is B

$a(b^2+c^2)=c(a^2+b^2)$

$\frac{b}{a}=\frac{c}{b}\Rightarrow =\frac{b^2}{a^2}=\frac{c^2}{b^2}$

$\Rightarrow \frac{b^2+a^2}{a^2}=\frac{c^2+b^2}{b^2}$

$\Rightarrow \frac{b^2+a^2}{a^2}=\frac{c^2+b^2}{ac}$

$\therefore c(b^2+a^2)=a(c^2+b^2)$