Question

If x=2+root 3,find the value of ( x+1 /x )whole cube

Answer 1

Answer:

x = 2+√3

(x+1 / x)³

[(2+√3) + 1 / 2+√3]³

[3+√3 / 2+√3]³

[3+√3 × 2-√3 / 2+√3 × 2-√3]³

[6-3√3+2√3-3 / 4-3]³

[3-√3/1]³

so,(a-b)³ = a³-b³-3ab(a-b)..........1

here, a=3 and b=√3

now, put values of a and b in 1

(3-√3) = (3)³ - (√3)³ - 3×3×√3 (3-√3)

          = 9-3√3-9√3(3-√3)

          = 9 - 3√3 - 9√3×3 + 9√3×√3

          = 9 - 3√3 - 27√3 + 27

          = 36 - 30√3

so, answer is 36 - 30√3

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