What are the solutions to the equation 6x^8+6=13x^4 ?

The solutions to the equation 6x^8+6=13x^4 are

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6x^8+6=13x^4

6 x^{8} + 6 = 13 x^{4}

x = \frac{3}{2}, x = - \frac{3}{2}, x = - \frac{3}{2}, x = - - \frac{3}{2}, x = \frac{2}{3}, x = - \frac{2}{3}, x = - \frac{2}{3}, x = - - \frac{2}{3}

Solution steps

6 x^{8} + 6 = 13 x^{4}

Move

13 x^{4}

to the left side

6 x^{8} + 6 - 13 x^{4} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

6 x^{8} - 13 x^{4} + 6 = 0

Rewrite the equation with

u = x^{2}, u^{2} = x^{4}

and

u^{4} = x^{8}

6 u^{4} - 13 u^{2} + 6 = 0

Solve

6 u^{4} - 13 u^{2} + 6 = 0 : u = \frac{3}{2}, u = - \frac{3}{2}, u = \frac{2}{3}, u = - \frac{2}{3}

u = \frac{3}{2}, u = - \frac{3}{2}, u = \frac{2}{3}, u = - \frac{2}{3}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{3}{2} : x = \frac{3}{2}, x = - \frac{3}{2}

Solve

x^{2} = - \frac{3}{2} : x = - \frac{3}{2}, x = - - \frac{3}{2}

Solve

x^{2} = \frac{2}{3} : x = \frac{2}{3}, x = - \frac{2}{3}

Solve

x^{2} = - \frac{2}{3} : x = - \frac{2}{3}, x = - - \frac{2}{3}

The solutions are

x = \frac{3}{2}, x = - \frac{3}{2}, x = - \frac{3}{2}, x = - - \frac{3}{2}, x = \frac{2}{3}, x = - \frac{2}{3}, x = - \frac{2}{3}, x = - - \frac{2}{3}

x^{3} - 7 x + 4 = 0

y, x = y^{3} - 6

x^{3} - 6 x^{2} + 13 x - 12 = 0

x^{2} - 5 x = 2 x^{3} - 4 x^{2} - x + 6

1200 = 600 x^{2} (3 - x)

What are the solutions to the equation 6x^8+6=13x^4 ?
The solutions to the equation 6x^8+6=13x^4 are
Find the zeros of 6x^8+6=13x^4
The zeros of 6x^8+6=13x^4 are