If x=3+2√2 thenq find the value of √x=1/√x
Answers
Answer:
√x + 1/√x = 2√2
Step-by-step explanation:
1st Method 2nd Method
Given x = 3 – 2√2 Given x = 3 – 2√2
⇒ x = 2 + 1 – 2√2 So, x + 1/x = 3 – 2√2 + 1/(3 – 2√2)
⇒ x = (√2)² + 1² – 2 × √2 × 1 = 3 – 2√2 + 3 + 2√2
⇒ x = (√2 – 1 )² = 6
∴ √x = (√2 – 1 ) Add 2 both sides
Now consider, (1/√x) = (1/(√2 – 1 ) x + 1/x + 2 = 6 + 2
Multiply and divide with (√2 + 1 ) (√x)² + (1/√x)² + 2 × √x × 1/√x = 8
We get (√x + 1/√x)² = 8
(1/√x) = (√2 + 1 )/[(√2 – 1 )(√2 + 1 )] √x + 1/√x = √8
= (√2 + 1 )/[2 – 1] √x + 1/√x = 2√2
∴ (1/√x) = (√2 + 1 )
√x + (1/√x) = (√2 – 1) + (√2 + 1)
= 2√2