What are the solutions to the equation (z^2+7)^2+(z^2+7)-72=0 ?

The solutions to the equation (z^2+7)^2+(z^2+7)-72=0 are z=1,z=-1,z=4i,z=-4i

Find the zeros of (z^2+7)^2+(z^2+7)-72=0

The zeros of (z^2+7)^2+(z^2+7)-72=0 are z=1,z=-1,z=4i,z=-4i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(z^{2} + 7)^{2} + (z^{2} + 7) - 72 = 0

z = 1, z = - 1, z = 4 i, z = - 4 i

Solution steps

(z^{2} + 7)^{2} + (z^{2} + 7) - 72 = 0

Expand

(z^{2} + 7)^{2} + (z^{2} + 7) - 72 : z^{4} + 15 z^{2} - 16

z^{4} + 15 z^{2} - 16 = 0

Rewrite the equation with

u = z^{2}

and

u^{2} = z^{4}

u^{2} + 15 u - 16 = 0

Solve

u^{2} + 15 u - 16 = 0 : u = 1, u = - 16

u = 1, u = - 16

Substitute back

u = z^{2},

solve for

z

Solve

z^{2} = 1 : z = 1, z = - 1

Solve

z^{2} = - 16 : z = 4 i, z = - 4 i

The solutions are

z = 1, z = - 1, z = 4 i, z = - 4 i

y, x = (y - 1)^{3}

4 x^{3} - 7 x^{2} - 2 x = 0

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

x^{3} - 3 x = 3

v^{3} = 1

What are the solutions to the equation (z^2+7)^2+(z^2+7)-72=0 ?
The solutions to the equation (z^2+7)^2+(z^2+7)-72=0 are z=1,z=-1,z=4i,z=-4i
Find the zeros of (z^2+7)^2+(z^2+7)-72=0
The zeros of (z^2+7)^2+(z^2+7)-72=0 are z=1,z=-1,z=4i,z=-4i