Question

if 5x^2-6x-5=0 then find out (x-1/x)^2​

Answer 1

Answer :

(x - 1/x)² = 36/25

Solution :

• Given : 5x² - 6x - 5 = 0
• To find : (x - 1/x)²

We have ;

=> 5x² - 6x - 5 = 0

=> 5x² - 5 = 6x

=> 5(x² - 1) = 6x

=> (x² - 1)/x = 6/5

=> x²/x - 1/x = 6/5

=> x - 1/x = 6/5

Now ,

Squaring both the sides , we get ;

=> (x - 1/x)² = (6/5)²

=> (x - 1/x)² = 36/25

Hence , (x - 1/x)² = 36/25

Answer 2

Answer:

$\large► \sf \: GIVEN \: \: EQUATION : -$

$\sf \: 5 {x}^{2} - 6x - 5 = 0$

$\large► \sf \: TO \: \: FIND: -$

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

$\large► \sf \: SOLUTION : -$

$\sf \: 5 {x}^{2} - 6x - 5 = 0$

$\implies\sf \: 5 {x}^{2} - 5 =6x$

$\implies\sf \: \frac{5 {x}^{2} }{5x} - \frac{5}{5x} = \frac{6x}{5x}$

$\implies\sf \: x - \frac{1}{x} = \frac{6}{5}$

$\sf \: Squaring \: \: both \: \: sides -$

$\implies\sf \: \bigg(x - \frac{1}{x} \bigg)^{2} = \bigg(\frac{6}{5} \bigg)^{2}$

$\implies\sf \: \bigg(x - \frac{1}{x} \bigg)^{2} = \frac{36}{25}$