Question

If x=5-2 sqrt 6 , then find the value of sqrt(x) + 1/(sqrt(x))​

Answer 1

*Question:-

• If x=5-2 sqrt 6 , then find the value of sqrt(x) + 1/(sqrt(x))

*Answer:-

Given,

• x = 5 + 2√6

This can be re-written as

• x = √3² + √2² + 2×√3×√2
• => x = ( √3 +√2)²
• => √x = √3 + √2

Now,

• (x-1)/√x = [(5+2√6)-1]/(√3+√2)
• => (x-1)/√x = (4+2√6)/(√3+√2)

Rationalising denominator,

=> (x-1)/√x = 2(2+√6)(√3-√2)/(√3+√2)(√3-√2)

=> (x-1)/√x = 2(2+√6)(√3-√2)/(3–2) [By (a+b)(a-b)=a²-b²]

=> (x-1)/√x = 2(2√3–2√2+√18-√12)/1

=> (x-1)/√x = 2(2√3–2√2+3√2–2√3) = 2√2

=> (x-1)/√x = 2√2 Answer.

Hope it helps you a lot.