Question

x^4-10x^3 + 26x^2-10x+1=0​

Answer 1

Given equation, x

4

−10x

3

+26x

2

−10x+1=0

⟹(x

2

+x

−2

)–10(x+x

−1

)+26=0[dividing byx

2

]

Substitute x+x

−1

=y in the above equation

⟹(y

2

−2)−10y+26=0⟹y

2

−10y+24=0⟹(y−6)(y−4)=0

⟹x+x

−1

=y=4and6

⟹x

2

−6x+1=0andx

2

−4x+1=0

⟹x=3±2

2

andx=2±

3

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