SOLUTION: Quartic equations of the form {{{Ax^4+Bx^3+Cx^2+Bx+A=0}}}, (A does not equal 0), are reducible to quadratics using the substitution {{{u=x+1/x }}} and grouping terms appropriately.

Question 1126759: Quartic equations of the form , (A does not equal 0), are reducible to quadratics using the substitution and grouping terms appropriately. Solve for x given .
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Divide the whole equation by x^2. (We can do this because we can see by inspection that x=0 is not a root.)

is (x+1/x) squared. Use this to rewrite the expression on the left in the equation as a polynomial with "x+1/x" as the variable; then factor.

[group terms as appropriate; note the "-8" is now represented as "2...-10"]

[this is now a polynomial with "x+1/x" as the variable. Substitute u = x+1/x if it helps you see what is being done]

Now multiply each factor by x (to "un-do" the first step above where we divided the whole equation by x^2)

or

or
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