If 2[x^2+1/x^2]-2[x-1/x]-8=0, then what are the two values of x-1/x?

SSC CGL Model Paper 12

Question : 64 of 100

Marks: +1, -0

2[x^2+1/x^2]-2[x-1/x]-8=0

, then what are the two values of

x-1/x

Solution:

2[x^2+1/x^2]-2[x-1/x]-8=0

⇒(x^2+1/x^2)

=(x-1/x)+4

⇒x^2+1/x^2-2

=(x-1/x)+4-2

⇒(x-1/x)^2

=(x-1/x)+2

Let

x -1 /x=a

∴a^2=a+2

⇒a^2-a-2=0

⇒a^2-2a+a-2=0

⇒ a (a -2 ) +1( a - 2 ) = 0

⇒(a - 2 ) (a + 1 ) = 0

⇒ a = -1 ,2

∴x-1/x=-1,2

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