If frac{1}{{p + q}},;frac{1}{{r + p}},;frac{1 | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(b) Since $\frac{1}{{p + q}},\;\frac{1}{{r + q}}$ and $\frac{1}{{q + r}}$ are in $A.P.$

$	herefore $ $\frac{1}{{r + q}} - \frac{1}{{p + q}} = \fra

Vedclass · Accepted Answer

${p^2},\;{q^2},\;{r^2}$ are in $A.P.$

Vedclass · Answer

(b) Since $\frac{1}{{p + q}},\;\frac{1}{{r + q}}$ and $\frac{1}{{q + r}}$ are in $A.P.$

$	herefore $ $\frac{1}{{r + q}} - \frac{1}{{p + q}} = \frac{1}{{q + r}} - \frac{1}{{r + p}}$

$ \Rightarrow $ $\frac{{p + q - r - p}}{{(r + p)(p + q)}} = \frac{{r + p - q - r}}{{(q + r)(r + p)}}$

$ \Rightarrow $ $\frac{{q - r}}{{p + q}} = \frac{{p - q}}{{q + r}}$ or ${q^2} - {r^2} = {p^2} - {q^2}$

$	herefore $ $2{q^2} = {r^2} + {p^2}$

Therefore ${p^2},\;{q^2},\;{r^2}$ are in $A.P.$

If $\frac{1}{{p + q}},\;\frac{1}{{r + p}},\;\frac{1}{{q + r}}$ are in $A.P.$, then

Similar Questions

The solution of ${\log _{\sqrt 3 }}x + {\log _{\sqrt[4]{3}}}x + {\log _{\sqrt[6]{3}}}x + ......... + {\log _{\sqrt[{16}]{3}}}x = 36$ is

If $\tan \,n\theta = \tan m\theta $, then the different values of $\theta $ will be in

Let $S_n$ denote the sum of the first $n$ terms of an arithmetic progression. If $\mathrm{S}_{10}=390$ and the ratio of the tenth and the fifth terms is $15: 7$, then $S_{15}-S_5$ is equal to:

After inserting $n$, $A.M.'s$ between $2$ and $38$, the sum of the resulting progression is $200$. The value of $n$ is

Find the sum of integers from $1$ to $100$ that are divisible by $2$ or $5.$