Solve the equation by using the square root property.
-$$\left( t - \frac { 1 } { 6 } \right) ^ { 2 } = - \frac { 17 } { 36 }$$
A) $\left\{ - \frac { 11 } { 36 } \right\}$
B) $\left\{ \frac { 1 } { 6 } \pm \frac { \sqrt { 17 } } { 6 } i \right\}$
C) $\left\{ \frac { 1 } { 6 } \pm \frac { \sqrt { 17 } } { 6 } \right\}$
D) $\left\{ \frac { 1 - i \sqrt { 17 } } { 6 } \right\}$

Question

Quizplus · Accepted Answer

The equation involves a negative number under the square root, which indicates the presence of imaginary numbers. Taking the square root of both sides gives $t - \frac{1}{6} = \pm \sqrt{-\frac{17}{36}}$, which simplifies to $t = \frac{1}{6} \pm \frac{\sqrt{17}}{6}i$, matching choice B.

Solve the Equation by Using the Square Root Property (t−16)2=−1736\left( t - \frac { 1 } { 6 } \right) ^ { 2 } = - \frac { 17 } { 36 }(t−61​)2=−3617​

Solve the Equation by Using the Square Root Property $\left( t - \frac { 1 } { 6 } \right) ^ { 2 } = - \frac { 17 } { 36 }$