Question

For what value of p will $\frac{a^{r+1}+b^{r+1}}{a^r+b^r}$ be the G.M. of a and b.

• A. $-1$
• B. $-2$
• C. $\frac{-1}{2}$
• D. None of these

Answer 1

The correct option is C $\frac{-1}{2}$

G.M of $a,b=\sqrt{ab}\frac{a^{r+1}+b^{r+1}}{a^r+b^r}=a^{r+\frac{1}{2}}.b^{\frac{1}{2}}+b^{r+\frac{1}{2}}.a^{\frac{1}{2}}{a}^{r+\frac{1}{2}}(a^{\frac{1}{2}}-b^{\frac{1}{2}})=b^{r+\frac{1}{2}}(a^{\frac{1}{2}}-b^{\frac{1}{2}})a^{r+\frac{1}{2}}=b^{r+\frac{1}{2}}(a\ne b\ne 0)r+\frac{1}{2}=0r=-\frac{1}{2}$