Question

If x = 2 + √3 , find the value x^3 + 1/x^3 .

Answer 1

Answer:

As we see that the x has a power of 3 so we begin by cubbing the whole equation.

So we start solving like:

x+1x=3

(x+1x)3=33

x3+3.x2.1x+3.x.1x2+1x3=27

(x3+1x3)+3.x2.1x+3.x.1x2=27

x3+1x3+(3x+3x)=27

x3+1x3+3(x+1x)=27

x3+1x3+3×3=27

x3+1x3+9=27

x3+1x3=18

Therefore the answer is 18