Х^2+х^4-82*х^2=0

To solve the equation х^2 + х^4 - 82*х^2 = 0, we can simplify the equation and then factor it. First, we combine like terms:

х^4 - 81*х^2 = 0

Now, we factor out the common term х^2:

х^2*(х^2 - 81) = 0

Now, we have a product equal to zero. According to the zero product property, either the first factor is equal to zero OR the second factor is equal to zero:

х^2 = 0 OR х^2 - 81 = 0

If we solve the first equation, we find:

х^2 = 0

Taking the square root of both sides:

х = 0

If we solve the second equation, we find:

х^2 - 81 = 0

Adding 81 to both sides:

х^2 = 81

Taking the square root of both sides:

х = ±9

So the solutions to the equation х^2 + х^4 - 82*х^2 = 0 are х = -9, 0, and 9.