x^(-2) = 9
solve for x
Steps too
I first squared the x on both sides and I was left with x^(-1) = -3,3
but then what would the answer be for x?
the answer is supposed to be 1/3, -1/3 but I don't know why
x^(-2) = 9
Since, x^(-2) = 1/x^2
1/x^2 = 9
Multiply both sides by x^2
1 = 9x^2
1/9 = x^2
square root of both sides
+ - 1/3 = x
Meant to comment,
If you square x^-2,
x^-2 * x^-2 = x-4 = 1/x^4
1/^4 = 81
square root of both sides
1/x^2 = 9
You are back to the above.
To solve the equation x^(-2) = 9, you need to follow these steps:
Step 1: Start with the given equation: x^(-2) = 9.
Step 2: To eliminate the negative exponent, you can take the reciprocal of both sides. This gives us 1/(x^2) = 9.
Step 3: Multiply both sides of the equation by x^2 to isolate x. The equation becomes 1 = 9x^2.
Step 4: Divide both sides of the equation by 9 to solve for x^2: 1/9 = x^2.
Step 5: Take the square root of both sides to solve for x: x = ±√(1/9).
Step 6: Simplify the square root on the right side: x = ±1/3.
So, the solutions to the original equation x^(-2) = 9 are x = 1/3 and x = -1/3.
In your specific case, when you squared both sides of the equation, you made a mistake by not treating the negative exponent properly. Squaring x^(-2) should have given you x^(-4), not x^(-1). That's why you obtained incorrect values for x. You need to revisit Step 2 and proceed from there to correctly solve the equation.