Please help me. I am asking though question 3 time but all answer are wrong. Please help me.
Answers
Given x = 9 + 4√5, find √x - 1 / √x
√x = √(9 + 4√5)
√x = √(√5 + √4 + 2√(5x4))
√x = √(√5 + √4)2
√x = √5 + 2
1 / √x = 1 / (√5 + 2) rationalize we get
1 / √x = (√5 - 2)
∴ √x - 1 / √x = √5 + 2 - √5 + 2 = 4.
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Solution
i) Given: x=(9-4√5)
ii) ==> √x = √(9-4√5); let this = √a - √b
Squaring both sides, 9 - 4√5 = a + b - 2√(ab)
Equating the rational and irrational parts from both side, a+b = 9 and 2√(ab) = 4√5
By identity, (a - b) = |√{(a+b)² - 4ab}|
So, here (a - b) = |√(81 - 80)| = 1
Solving (a + b) = 9 and (a - b) = 1, a = 5 and b = 4
Thus, √x = √5 - 2
iii) 1/√x = 1/(√5 - 2) = (√5 + 2) [By rationalizing the denominator]
iv) Hence, √x + 1/√x = (√5 - 2) - (√5 + 2) = -4
Square root symbol was found missing in these two steps, which now have been corrected.
"By identity, (a - b) = |√{(a+b)² - 4ab}|
So, here (a - b) = |√(81 - 80)| = 1"