x²+x-² = 1 it's x square + x -2
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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
= 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
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