Question

If x square - 5x = 1 find x square + 1/x square

Answer 1

Answer :

27

Step-by-step explanation :

x² - 5x = 1

⇒ x² = 5x + 1

On dividing both sides by x.

⇒ x = 5 + 1 / x

⇒ x - 1/x = 5

Now, on squaring both sides,

(x - 1/x )² = (5)²

⇒ x² + 1/x² - 2 = 25

⇒ x² + 1/x² = 25 + 2

⇒ x² + 1/x² = 27

Hence, the value of x² + 1/x² is 27.

Answer 2

Answer: 27

Step-by-step explanation:

Given,

x² -5x = 1

x²  = 1 + 5x

Taking x common in RHS,

x²  = x( 1/x +5)

Canceling  out  x from both sides,

x = (1/x + 5)

x - 1/x  = 5

Making square of  both sides,

(x - 1/x )² = 5²

x² + 1/x² -(2 × x × 1/x) = 25

x² + 1/x² - 2 = 25

x² + 1/x² = 25 + 2

x² + 1/x² = 27

Note:

(a+b)² = a² + b² +2ab

(a-b)² = a² + b² -2ab