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35x^4+2x^2-1=0
What is the value of x?
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This equation is called biquadratic (the degrees of the unknown "x" are 4, 2 and zero).
The method of solving such equations is as follows:
Introduce new variable y = x^2. Then your equation takes the form
35y^2 + 2y - 1 = 0.
It is just a quadratic equation, and you can apply the quadratic formula to solve it:
= = = .
= = . = = .
Since y = x^2, we are interested in positive "y" only.
Thus we have x^2 = and, hence, x = +/- = +/-.
Answer. The two real roots of the original equation are +/-.
See the lesson
- Solving polynomial equations of high degree by introducing a new variable
in this site.