Question

if x+1/x=5 find the value of ✓x+1/✓x is equal to​

Answer 1

Question:-

If x + 1/x = 5, find √x + 1/√x

Formula used:-

• (a + b)² = a² + b² + 2ab

Answer:-

To find: √x + 1/√x

Squaring whole term

(√x + 1/√x)² = (√x)² + (1/√x)² + (2 * √x * 1/√x)

=> (√x + 1/√x)² = x + 1/x + 2

We have the value of (x + 1/x) which is equal to 5

=> (√x + 1/√x)² = 5 + 2

=> (√x + 1/√x)² = 7

Taking square root both sides

=> √x + 1/√x = ±√7

Ans. (√x + 1/√x) = ±√7

Note:-

±y means +y and -y

After taking square root the value in R.H.S will be ±√7. We can understand this by an example:-

Suppose a² = 5

Then a = ±√5

This is because both +√5 and -√5 will satisfy the equation.

(+√5)² = 5 and,

(-√5)² = 5 [ - * - = +]