if x+1/x=2 then find the value of (x-1/x)^3
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Given :
- x + 1/x = 2
To Find :
- Value of ( x - 1/3 )³
Solution :
→ x + 1/x = 2
→ x² + 1 = 2x
→ x² - 2x + 1 = 0
→ x² - 1x - 1x + 1 = 0
→ x ( x - 1 ) - 1 ( x - 1 ) = 0
→ ( x - 1 ) ( x - 1 ) = 0
→ x = 1
Put value of x in ( x - 1/3 )³
→ ( 1 - 1/3 )³
→ [ ( 3 - 1 )/3 ]³
→ ( 2/3 )³
→ 8/27
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