What are the solutions to the equation 4y^6+3y^4-7y^2+20=0 ?

The solutions to the equation 4y^6+3y^4-7y^2+20=0 are No Solution for y\in\mathbb{R}

Find the zeros of 4y^6+3y^4-7y^2+20=0

The zeros of 4y^6+3y^4-7y^2+20=0 are No Solution for y\in\mathbb{R}

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4 y^{6} + 3 y^{4} - 7 y^{2} + 20 = 0

No Solution for y \in R

Solution steps

4 y^{6} + 3 y^{4} - 7 y^{2} + 20 = 0

Rewrite the equation with

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

and

u^{3} = y^{6}

4 u^{3} + 3 u^{2} - 7 u + 20 = 0

Solve

4 u^{3} + 3 u^{2} - 7 u + 20 = 0 : u \approx - 2.37415 \dots

u \approx - 2.37415 \dots

Substitute back

u = y^{2},

solve for

y

Solve

y^{2} = - 2.37415 \dots :

No Solution for

y \in R

The solution is

No Solution for y \in R

x^{4} + 5 = 0

x^{37} = 2500 (7.5)^{37}

x^{4} - 18 x - 10 = 0

64 = x^{6}

x^{3} + 3 x^{2} - 33 x - 35 = 0

What are the solutions to the equation 4y^6+3y^4-7y^2+20=0 ?
The solutions to the equation 4y^6+3y^4-7y^2+20=0 are No Solution for y\in\mathbb{R}
Find the zeros of 4y^6+3y^4-7y^2+20=0
The zeros of 4y^6+3y^4-7y^2+20=0 are No Solution for y\in\mathbb{R}