Question

Sum of two numbers is equal to the sum of their reciprocal. Show that they are also the reciprocal of each other.​

Answer 1

Answer:

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Answer 2

Answer :–

GIVEN :–

• Sum of two numbers is equal to the sum of their reciprocal.

TO PROVE :–

• They numbers are also the reciprocal of each other.

SOLUTION :–

• Let the numbers are 'P' and 'Q' .

• According to the question –

$\\ \implies \: \: { \bold{sum \: \: of \: \: numbers = sum \: \: of \: \: reciprocal \: \: of \: \: numbers}}$

$\\ \implies \: \: { \bold{P + Q = \dfrac{1}{P} + \dfrac{1}{Q} }}$

$\\ \implies \: \: { \bold{P + Q = \dfrac{P + Q }{P. Q } }}$

$\\ \implies \: \: { \bold{ {\cancel{(P + Q )}}= \dfrac{ \cancel{(P + Q) }}{PQ } }}$

$\\ \implies \: \: { \bold{1= \dfrac{ 1}{PQ } }}$

$\\ \implies \: \: { \bold{PQ= 1}}$

$\\ \implies \: \: { \bold{P= \dfrac{1}{Q} \: \: and \: \: Q= \dfrac{1}{P}}}$

• So that , Numbers are reciprocal.

$\\ \longrightarrow \: \: { \bold{ \underline{ \underline{Hence \: \: proved}}}}$

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