2015 · Q8
If x={3}+{2}, then the value of x³+x+1/x+1/x³ is
Elementary MathematicsAlgebra
- A10{3}
- B20{3}
- C10{2}
- D20{2}
Explanation
1/x = 1/(sqrt(3) + sqrt(2)) = sqrt(3) - sqrt(2), so x + 1/x = 2*sqrt(3). Then x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x) = 24*sqrt(3) - 6*sqrt(3) = 18*sqrt(3). Adding gives 18*sqrt(3) + 2*sqrt(3) = 20*sqrt(3). Hence option (b).