What are the solutions to the equation 8y^2=-15-y^4 ?

The solutions to the equation 8y^2=-15-y^4 are y=sqrt(5)i,y=-sqrt(5)i,y=sqrt(3)i,y=-sqrt(3)i

Find the zeros of 8y^2=-15-y^4

The zeros of 8y^2=-15-y^4 are y=sqrt(5)i,y=-sqrt(5)i,y=sqrt(3)i,y=-sqrt(3)i

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8 y^{2} = - 15 - y^{4}

y = 5 i, y = - 5 i, y = 3 i, y = - 3 i

Solution steps

8 y^{2} = - 15 - y^{4}

Switch sides

- 15 - y^{4} = 8 y^{2}

Move

8 y^{2}

to the left side

- 15 - y^{4} - 8 y^{2} = 0

Write in the standard form

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

- y^{4} - 8 y^{2} - 15 = 0

Rewrite the equation with

u = y^{2}

and

u^{2} = y^{4}

- u^{2} - 8 u - 15 = 0

Solve

- u^{2} - 8 u - 15 = 0 : u = - 5, u = - 3

u = - 5, u = - 3

Substitute back

u = y^{2},

solve for

y

Solve

y^{2} = - 5 : y = 5 i, y = - 5 i

Solve

y^{2} = - 3 : y = 3 i, y = - 3 i

The solutions are

y = 5 i, y = - 5 i, y = 3 i, y = - 3 i

x^{4} - 4 x^{2} - 3 x + 5 = 0

\frac{x ^{4}}{8 + 1} = 33

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

x^{6} + 2 x^{3} + 1 = 0

2 x^{4} - 26 x^{2} + 72 = 0

What are the solutions to the equation 8y^2=-15-y^4 ?
The solutions to the equation 8y^2=-15-y^4 are y=sqrt(5)i,y=-sqrt(5)i,y=sqrt(3)i,y=-sqrt(3)i
Find the zeros of 8y^2=-15-y^4
The zeros of 8y^2=-15-y^4 are y=sqrt(5)i,y=-sqrt(5)i,y=sqrt(3)i,y=-sqrt(3)i