Question

if x+ √5+2 then find x -1/x​

Answer 1

Solution :-

Correct will be x if x = √5 + 2 .

Then 1/x = 1 / √5 + 2 .

Let's rationalise its denominator .

⇒ 1/x = 1 / √5 + 2.

⇒ 1/x = (√5 - 2) / [ (√5 + 2) (√5 - 2 ) ]

⇒ 1/x = √5 - 2 / (√5)² -(2)² .

Using ,

• a² - b² = ( a + b ) ( a - b ) .

⇒ 1/x = √5 - 2 / 5 - 4 .

⇒ 1/x = √5 - 2 / 1 .

Now subtract x and 1/x .

= √5 + 2 - [ √5 - 2 ] .

= √5 + 2 - √5 + 2 .

= 4 .

Hence the required answer is 4 .