If x=5-root21divided by 2,find x^2+1/x^2
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X = (5 – r(21)) ÷ 2
1/X = 2÷(5–r(21)) = 2(5+r(21))÷4 = (5+r(21))÷2
X + 1/X = (5–r(21))/2 + (5+r(21))/2 = 5
X + 1/X = 5
Squaring on both sides
X² + 1/X² + 2×X×1/X = 25
X² + 1/X² = 23
1/X = 2÷(5–r(21)) = 2(5+r(21))÷4 = (5+r(21))÷2
X + 1/X = (5–r(21))/2 + (5+r(21))/2 = 5
X + 1/X = 5
Squaring on both sides
X² + 1/X² + 2×X×1/X = 25
X² + 1/X² = 23
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