Question

If x = sqrt(3) + 2 , then find the value of x ^ 2 + x - 4sqrt(3)

Answer 1

Step-by-step explanation:

It is given that,

x=2−3

so,

1/x=1/(2−3)

By rationalizing the denominator, we get

=[1(2+3)]/[(2−3)(2+3)]

=[(2+3)]/[(22)−(3)2]

=[(2+3)]/[4−3]

=2+3

Now,

x−1/x=2−3−2−3

=−23

Let us cube on both sides, we get

(x−1/x)3=(−23)3

x3−1/x3−3(x)(1/x)(x−1/x)=243

x3−1/x

Answer 2

$x =\sqrt{3} +2\\then \ find \ the\ value\ of \\x^{2} - 4\sqrt{3} \\=(\sqrt{3} +2)^{2} - 4\sqrt{3}\\=3\ + 4\sqrt{3} + 4 -4\sqrt{3} \\=3+4\\=7$