1.

If x = 9 + 4v5find the value of √x-1/√x​

Answer»

Answer:

4

Step-by-step EXPLANATION:

→ x = 9 + 4√5

→ x = 5 + 4 + 4√5

→ x = (√5)² + (√4)² + 2*2*√5

→ x = (√5)² + (2)² + 2*2*√5

(a+b)² = a² + b² + 2*a*b

→ x = (√5 + 2)²

→ √x = √5 + 2

→ 1/√x = 1/(√5 + 2)

Multiply as well as divide by √5 - 2:

→ 1/√x = (√5 - 2)/(√5 + 2)(√5 - 2)

→ 1/√x = (√5 - 2)/(√5² - 2²)

→ 1/√x = (√5 - 2)/(5-4) = √5 - 2

Thus,

= > √x - 1/√x

= > √5 + 2 - (√5 - 2)

= > 4


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