If x+1/x=2 then x^8+1/x^8
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Answer is 2.
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EXPLANATION.
⇒ (x + 1/x) = 2.
As we know that,
Formula of :
⇒ (a + b)² = a² + b² + 2ab.
Using this formula in this question, we get.
Squaring on both sides of the equation, we get.
⇒ (x + 1/x)² = (2)².
⇒ (x)² + (1/x)² + 2(x)(1/x) = 4.
⇒ x² + 1/x² + 2 = 4.
⇒ x² + 1/x² = 4 - 2.
⇒ x² + 1/x² = 2.
Again, squaring on both sides of the equation, we get.
⇒ (x² + 1/x²)² = (2)².
⇒ (x²)² + (1/x²)² + 2(x²)(1/x²) = 4.
⇒ x⁴ + 1/x⁴ + 2 = 4.
⇒ x⁴ + 1/x⁴ = 4 - 2.
⇒ x⁴ + 1/x⁴ = 2.
Now, again squaring on both sides of the equation, we get.
⇒ (x⁴ + 1/x⁴)² = (2)².
⇒ (x⁴)² + (1/x⁴)² + 2(x⁴)(1/x⁴) = 4.
⇒ x⁸ + 1/x⁸ + 2 = 4.
⇒ x⁸ + 1/x⁸ = 4 - 2.
⇒ x⁸ + 1/x⁸ = 2.
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