The roots of the equation $ \displaystyle x^{-2}+x^{-1}=12 $
- $ \displaystyle \frac{1}{2},-\frac{1}{3} $
- $ \displaystyle \frac{1}{3},-\frac{1}{4} $
- $3,-3$
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None of these
Reveal answer
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B
Correct answer
Explanation
Let u = 1/x. Then u^2 + u = 12, so u^2 + u - 12 = 0. (u+4)(u-3) = 0. u = -4 or u = 3. Since u = 1/x, x = -1/4 or x = 1/3.
AI explanation
To solve the equation x^-2 + x^-1 = 12, we substitute y = 1/x, which gives the quadratic equation y squared plus y equals 12. Rearranging this to the standard form yields y squared plus y minus 12 equals zero. Factoring this quadratic gives (y + 4)(y - 3) = 0, so the values for y are -4 and 3. Reverting back to x by using x = 1/y gives the roots x = 1/3 and x = -1/4.