x=2+√3 find x^2+1/x^2
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Answered by
0
Heya ☺
Given that
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
= 7 + 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
Thanks
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Answered by
0
Step-by-step explanation:
1/x=1/2+√3
=2-√3/1
=2-√3
x2+1/x²
4+3+4√3+4+3-4√3
=14
hope it helps
thanx
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