Question

solve the equation 6x⁴-35x³+62x²-35x+6=0​

Answer 1

Answer:

Step-by-step explanation:

6x^2 - 35x + 62 - 35/x + 6/x^2 = 0

6x^2 + 6/x^2 - 35x - 35/x + 62 = 0

6(x^2 + 1/x^2) - 35(x + 1/x) + 62 = 0

Now use the substitution y = x + 1/x, y^2 = x^2 + 1/x^2 + 2

6(y^2 - 2) - 35y + 62 = 0

6y^2 - 35y + 50 = 0

(3y - 10) (2y - 5) = 0

y = 10/3

x + 1/x = 10/3

x = 1/3 and x = 3

y = 5/2

x + 1/x = 5/2

x = 1/2 and x = 2.

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