Question

YOU SHOULD NOT USE BINOMIAL THEOREM OR FIND THE VALUE OF X TO FIND THE ANSWER !!!!!
YOU SHOULD FIND THE ANSWER BY USING IDENTIES ONLY .
WHO ANSWERS FRIST AND CORRECT WILL BE MARKED BRAINLIEST​

Answer 1

★ᏀᏆᏙᎬΝ:-

$\sf x + \dfrac{1}{x} = 5$

★Ͳϴ ҒᏆΝᎠ:-

$\sf \sqrt{x} + \dfrac{1}{ \sqrt{x}}$

★Solution:-

Squaring $\sf \sqrt{x} + \dfrac{1}{ \sqrt{x}}$ and using identity $\sf (a+b)^2 = a^2 + b^2 + 2ab$ will give

$\sf \implies \Bigg ( \sqrt{x} + \dfrac{1}{ \sqrt{x}} \Bigg )^2 = ( \sqrt{x} )^2 + \Bigg ( \dfrac{1}{ \sqrt{x}} \Bigg )^2 + 2 \times \sqrt{x} \times \dfrac{1}{ \sqrt{x}}$

$\sf \implies \Bigg ( \sqrt{x} + \dfrac{1}{ \sqrt{x}} \Bigg )^2 = x +\dfrac{1}{x} + 2$

$\sf \implies \Bigg ( \sqrt{x} + \dfrac{1}{ \sqrt{x}} \Bigg )^2= 5 + 2$

$\sf \implies \Bigg ( \sqrt{x} + \dfrac{1}{ \sqrt{x}} \Bigg )^2= 7$

$\sf \implies \sqrt{x} + \dfrac{1}{ \sqrt{x}}= \sqrt{7}$

$\boxed{ \sqrt{x} + \dfrac{1}{ \sqrt{x}} = \sqrt{7}}$

Hope it helps.