Question

if X=9+4√5 find the value of √x-(1/√x)
Pls answer it's urgent HHW Karna hai lol​

Answer 1

Answer:

√x - 1/√x = 4

Step-by-step explanation:

x = 9 + 4√5

(i) √x = √(9 + 4√5)      [∵ it can be written as (2 + √5)²) ]

= √[(2)² + 2(2)(√5) + (√5)²]

√x = √(2 + √5)²

∴ √x = 2 + √5

(ii) 1/√x = 1/2 + √5

Rationalizing The Denominator,

= 1/2 + √5 × 2 - √5/2 - √5

= 2 - √5/(2 + √5)(2 - √5)

= 2 - √5/(2)² - (√5)²

= 2 - √5/4 - 5

= 2 - √5/-1

= -(2 - √5)

= -2 + √5

∴ 1/√x = -2 + √5

ATQ,

√x - 1/√x = 2 + √5 - (-2 + √5)

= 2 + √5 + 2 - √5

√x - 1/√x = 4

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