Question

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

• A. $a(b^2+a^2)$ = $c(b^2+c^2)$
• B. $a(b^2+c^2)$ = $c(a^2+b^2)$
• C. $a^2(b+c)$ = $c^2(a+b)$
• D. $b^2=\frac{a}{c}$

Answer 1

The correct option is B

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

If $a,b,c$ are in G.P., then $b^2=ac.$

$\Rightarrow b^2(a-c)=ac(a-c)$

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

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

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