Question

16. If x = 2+√3, find the value of xc²+ 22
x²= 2 + 3​

Answer 1

Answer:

x=2+√3

1/x=1/2+√3

1×(2-√3)/(2+√3)(2-√3)

(2-√3)/(2^2-√3^2)

(2-√3)/4-3

(2-√3)

Therefore

x^2 = (2+√3)

2^2+(√3)^2+2×2×√3

4+3+4√3

1/x^2 = (2-√3)^2

2^2+(√3)^2-2×2×√3

4+3-4√3

7-4√3

x^2+1/x^2

(7+4√3)+(7-4√3)

7+4√3+7-4√3

7+7+4√3-4√3

=14

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