What are the solutions to the equation 20u^4-13u^2+2=0 ?

The solutions to the equation 20u^4-13u^2+2=0 are u=sqrt(2/5),u=-sqrt(2/5),u= 1/2 ,u=-1/2

Find the zeros of 20u^4-13u^2+2=0

The zeros of 20u^4-13u^2+2=0 are u=sqrt(2/5),u=-sqrt(2/5),u= 1/2 ,u=-1/2

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

u = \frac{2}{5}, u = - \frac{2}{5}, u = \frac{1}{2}, u = - \frac{1}{2}

Solution steps

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

Rewrite the equation with

v = u^{2}

and

v^{2} = u^{4}

20 v^{2} - 13 v + 2 = 0

Solve

20 v^{2} - 13 v + 2 = 0 : v = \frac{2}{5}, v = \frac{1}{4}

v = \frac{2}{5}, v = \frac{1}{4}

Substitute back

v = u^{2},

solve for

u

Solve

u^{2} = \frac{2}{5} : u = \frac{2}{5}, u = - \frac{2}{5}

Solve

u^{2} = \frac{1}{4} : u = \frac{1}{2}, u = - \frac{1}{2}

The solutions are

u = \frac{2}{5}, u = - \frac{2}{5}, u = \frac{1}{2}, u = - \frac{1}{2}

x^{3} + 2 x^{2} + 4 x - 8 = 0

445 = 5 x^{3}

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

t^{3} - 13 t^{2} + 65 t - 105 = 0

2 x^{3} - 3 x^{2} + 32 x + 17 = 0

What are the solutions to the equation 20u^4-13u^2+2=0 ?
The solutions to the equation 20u^4-13u^2+2=0 are u=sqrt(2/5),u=-sqrt(2/5),u= 1/2 ,u=-1/2
Find the zeros of 20u^4-13u^2+2=0
The zeros of 20u^4-13u^2+2=0 are u=sqrt(2/5),u=-sqrt(2/5),u= 1/2 ,u=-1/2