What is x^2-1=0,y^2+z=0,z^2+y=0 ?

The solution to x^2-1=0,y^2+z=0,z^2+y=0 is

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Popular >

x^2-1=0,y^2+z=0,z^2+y=0

Solution

x^{2} - 1 = 0, y^{2} + z = 0, z^{2} + y = 0

Solution

x = 1, x = 1, x = 1, x = 1, y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i, z = 0 z = - 1 z = \frac{1}{2} + i \frac{3}{2} z = \frac{1}{2} - i \frac{3}{2}

Solution steps

x^{2} - 1 = 0 y^{2} + z = 0 z^{2} + y = 0

Isolate

z

for

y^{2} + z = 0 : z = - y^{2}

Plug the solutions

z = - y^{2}

into

z^{2} + y = 0

For

z^{2} + y = 0

, subsitute

z

with

- y^{2} : y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i

Plug the solutions

y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i

into

y^{2} + z = 0

For

y^{2} + z = 0

, subsitute

y

with

0 : z = 0

For

y^{2} + z = 0

, subsitute

y

with

- 1 : z = - 1

For

y^{2} + z = 0

, subsitute

y

with

\frac{1}{2} - \frac{3}{2} i : z = \frac{1}{2} + i \frac{3}{2}

For

y^{2} + z = 0

, subsitute

y

with

\frac{1}{2} + \frac{3}{2} i : z = \frac{1}{2} - i \frac{3}{2}

x^{2} - 1 = 0 : x = 1, x = - 1

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x^{2} - 1 = 0, y^{2} + z = 0, z^{2} + y = 0

are

x = 1, x = 1, x = 1, x = 1, y = 0, y = - 1, y = \frac{1}{2} - \frac{3}{2} i, y = \frac{1}{2} + \frac{3}{2} i, z = 0 z = - 1 z = \frac{1}{2} + i \frac{3}{2} z = \frac{1}{2} - i \frac{3}{2}

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Frequently Asked Questions (FAQ)

What is x^2-1=0,y^2+z=0,z^2+y=0 ?
The solution to x^2-1=0,y^2+z=0,z^2+y=0 is