# Biquadratic Equations

Biquadratic equations are quartic equations with no odd-degree terms:

**ax ^{4} + bx^{2} + c = 0**

### Solving Biquadratic Equations

To solve biquadratic equations, change **x ^{2} = t, x^{4} = t^{2}; **this generates a quadratic equation with the unknown,

**t**:

**at ^{2} + bt + c = 0 **

For every positive value of **t** there are **two values of x**, find:

The same procedure can be used to solve the equations of the type:

ax^{6} + bx^{3} + c = 0

ax^{8} + bx^{4} + c = 0

ax^{10} + bx^{5} + c = 0

#### Examples

x^{4} − 10x^{2} + 9 = 0

x^{4} − 10x^{2} + 9

x^{2} = t

x^{4} − 10x^{2} + 9 = 0

t^{2} − 10t + 9 = 0

x^{4} − 61x^{2} + 900 = 0

x^{4} − 25x^{2} + 144 = 0

x^{4} − 16x^{2} − 225 = 0

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