if x = 9+4√5 then find the value of √x-1÷√-x
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x = 9 + 4√5
=> √x = √(9 + 4√5)
=> √x = √(√5 + √4 + 2√(5x4))
=> √x = √(√5 + √4)^2
=> √x = √5 + 2
Now,
1 / √x = 1 / (√5 + 2)
By rationalizing, we get:-
1 / √x = (√5 - 2)
=> √x - 1 / √x = √5 + 2 - √5 + 2 = 4
Hence,the required answer is 4.
=> √x = √(9 + 4√5)
=> √x = √(√5 + √4 + 2√(5x4))
=> √x = √(√5 + √4)^2
=> √x = √5 + 2
Now,
1 / √x = 1 / (√5 + 2)
By rationalizing, we get:-
1 / √x = (√5 - 2)
=> √x - 1 / √x = √5 + 2 - √5 + 2 = 4
Hence,the required answer is 4.
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