If x = 2 + √3 then find the value of x3/2 + 1/(x3/2) = ?
x = 2 + √3 Then, 1/x = 2 - √3 x+ 1/x = 2 + √3 + 2 - √3 x+ 1/x = 4 Let √x + 1/√x = P Squaring on both sides, we will get x + 1/x + 2 = P2 4+ 2 = P2 So P =√6 hence √x + 1/√x = √6 = N So now (√x)3 + (1/√x)3 = N3-3N = (√6)3-3(√6) = 6√6 - 3√6 = 3√6
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