Question

if x+1/x=6, find the value of. 1.(x-1/x) 2.(x^2 - 1/x^2)
Can u plss solve this problem
Its urgent plss
Expansion lesson class 9th ​

Answer 1

Topic

• Identity

An identity is an equation that is always true.

Solution (I)

Given Expression

$\implies x+\dfrac{1}{x} =6$

$\implies (x+\dfrac{1}{x} )^{2}=6^{2}$

$\implies x^{2}+2+\dfrac{1}{x^{2}} =36$

We can use identity here to find the required answer.

$(x-\dfrac{1}{x} )^{2}=x^{2}-2+\dfrac{1}{x^{2}}$

To find the value we need to subtract 4.

$\implies x^{2}-2+\dfrac{1}{x^{2}} =32$

$\implies (x-\dfrac{1}{x} )^{2}=32$

Now using square root we get the answer.

$\therefore x-\dfrac{1}{x} =\pm 4\sqrt{2}$

This is the required answer.

Solution (II)

Given Expression

$\implies x^{2}-\dfrac{1}{x^{2}}=(x+\dfrac{1}{x} )(x-\dfrac{1}{x} )$

$\implies x^{2}-\dfrac{1}{x^{2}}=6\times (\pm 4\sqrt{2} )$

$\therefore x^{2}-\dfrac{1}{x^{2}}=\pm 24\sqrt{2}$

This is the required answer.

Answer 2

Given :-

$\sf\bigg\lgroup x+\dfrac{1}{x}\bigg\rgroup = 6$

To Find :-

Value of

$\sf (i)\bigg\lgroup x-\dfrac{1}{x}\bigg\rgroup$

$\sf (ii)\bigg\lgroup x^2-\dfrac{1}{x^2}\bigg\rgroup$

Solution :-

(i)

$\sf\bigg(x+\dfrac{1}{x}\bigg)=6$

On squaring both sides

$\sf \bigg(x+\dfrac{1}{x}\bigg)^2= (6)^2$

Apply identity = (a + b)² = a² + 2ab + b²

$\sf x^2+2(x)\bigg(\dfrac{1}{x}\bigg) + \bigg(\dfrac{1}{x}\bigg)^2=36$

$\sf x^2+2+\dfrac{1}{x^2}=36$

$\sf x^2 + \dfrac{1}{x^2}=36-2$

$\sf x^2+\dfrac{1}{x^2}=34$

Similarly

$\sf \bigg(x-\dfrac{1}{x}\bigg)^2 = x^2 + \dfrac{1}{x^2} - 2\times a\times\dfrac{1}{a}$

Putting x² + 1/x² = 34

$\sf \bigg(x-\dfrac{1}{x}\bigg)^2=34-2\times 1$

$\sf \bigg(x-\dfrac{1}{x}\bigg)^2=32$

$\sf \bigg(x-\dfrac{1}{x}\bigg)=\sqrt{32}$

$\sf\bigg(x-\dfrac{1}{x}\bigg)=\pm 4\sqrt{2}$

(ii)

$\sf\bigg(x^2-\dfrac{1}{x^2}\bigg)$

Apply the identity = (a² - b²) = (a + b)(a - b)

$\sf \bigg(x^2-\dfrac{1}{x^2}\bigg)=\bigg(x + \dfrac{1}{x}\bigg)\bigg(x-\dfrac{1}{x}\bigg)$

As we have find above the value of x + 1/x and x - 1/x

$\sf\bigg(x^2-\dfrac{1}{x^2}\bigg)=(\pm 4\sqrt{2})(6)$

$\sf\bigg(x^2-\dfrac{1}{x^2}\bigg)=(\pm 24\sqrt{2})$