Question

if x-1/x=3/2 find the value of a) x+1/x
​

Answer 1

Answer:

squaring both side

x^2+1/x^2-2=9/4

x^2+1/x^2=17/4

add 2 both side

x^2+1/x^2+2=25/4

(x+1/x)^2=25/4

x+1/x=5/4

Answer 2

Answer:

Given,

$\large \color{red}{ \bold{★ \: \: \: \: x - \frac{1}{x} = \frac{3}{2} }}$

To find :—

$\color{violet} \bold{→x + \frac{1}{x} = ?}$

Now,

$\color{blue}\bold{(x + \frac{1}{x} ) ^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2.x. \frac{1}{x} }$

$\color{blue} \bold{ \implies {(x + \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2.x. \frac{1}{x} + 4.x. \frac{1}{x} }$

$\color{blue} \bold{ \implies {(x + \frac{1}{x}) }^{2} = {(x - \frac{1}{x} )}^{2} + 4.x. \frac{1}{x} }$

$\color{blue} \bold{ \implies {(x + \frac{1}{x}) }^{2} = {(x - \frac{1}{x} )}^{2} + 4 }$

$\color{blue} \bold{ \implies {(x + \frac{1}{x}) }^{2} = {( \frac{3}{2} )}^{2} + 4 }$

$\color{blue} \bold{ \implies {(x + \frac{1}{x}) }^{2} = \frac{9}{4} + 4 }$

$\color{blue} \bold{ \implies {(x + \frac{1}{x}) }^{2} = \frac{9 + 16}{4} }$

$\color{blue} \bold{ \implies {(x + \frac{1}{x}) }^{2} = \frac{25}{4} }$

$\color{blue} \bold{ \implies \sqrt{{(x + \frac{1}{x}) }^{2}} = \sqrt{\frac{25}{4} }}$

$\large{\color{orange} \bold{ \implies \boxed {\bold{x + \frac{1}{x} = \frac{5}{2} }}}}$

Formula required :—

$\boxed{ \bold{† \: {(x + y)}^{2} = {(x - y)}^{2} + 4xy}}$