Question

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

• A. $a^2, b^2, c^2$ are in G.P.
• B. $a^2 (b + c),c^2 (a + b),b^2 (a + c)$ are in G.P.
• C. $\frac{a}{b+c} , \frac{b}{c+a}, \frac{c}{a+b}$ are in G.P.
• D. None of these

Answer 1

Answer: (A)

$a^2, b^2, c^2$ are in G.P.

Answer 2

$\because a, b, c$ are in G.P.
$\therefore \frac{b}{a} = \frac{c}{b} =r$
$\Rightarrow \frac{b^{2}}{a^{2}} = \frac{c^{2}}{b^{2}} =r^{2}$
$\Rightarrow \frac{b^{2}}{a^{2}} = \frac{c^{2}}{b^{2}} =r^{2}$
$\Rightarrow a^{2} , b^{2} , c^{2}$ are in G.P.