if x+1/x=2,find X2+1/X2 and x4+1/x4
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EXPLANATION.
⇒ x + 1/x = 2.
As we know that,
Squaring on both sides of the equation, we get.
⇒ (x + 1/x)² = (2)².
⇒ (x² + 1/x² + 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.
⇒ [x⁴ + 1/x⁴ + 2(x²)(1/x²)] = 4.
⇒ [x⁴ + 1/x⁴ + 2] = 4.
⇒ x⁴ + 1/x⁴ = 4 - 2.
⇒ x⁴ + 1/x⁴ = 2.
Value of :
x² + 1/x² = 2 & x⁴ + 1/x⁴ = 2.
Answered by
41
Squaring Both Side :
- Because (a + b)² = a² + b² + 2ab
Squaring Both Side :
- Because (a + b)² = a² + b² + 2ab
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