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प्रश्न
Solve the equation
6x4 – 35x3 + 62x2 – 35x + 6 = 0
उत्तर
This is Type I even degree reciprocal equation.
Hence it can be rewritten as
`6(x^2 + 1/x^2) - 35(x + 1/x) + 62` = 0 ......(1)
y = `x + 1/x`
y2 = `x^2 + 1/x^2 + 2`
y2 – 2 = x^2 + 1/x^2`
(1) ⇒ 6(y2 – 2) – 35y + 62 = 0
6y2 – 12 – 35y + 62 = 0
6y2 – 35y + 50 = 0
`(y - 5/2)(y - 10/3)` = 0
y = `5/2` or y = `10/3`
`x + 1/x = 5/2` or `x + 1/x = 10/3`
`(x^2 + 1)/x = 5/2` or `(x^2 + 1)/x = 10/3`
2x2 + 2 – 5x = 0 or 3x2 + 3 = 10x
2x2 – 5x + 2 = 0 or 3x2 – 10x + 3 = 0
x = `2, 1/2` or x = `3, 1/3`
Roots are `2, 1/2, 3` and `1/3`
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