Question

Use the square root property of equality to solve (x  – 3)2 = –4. The solutions are a. -1 or 7 b. 1 or 5 c. 3+- 2i d. 3+-4i

Answer 1

Answer:

The solution is    3 ± 2i .   The correct option is C.

Step-by-step explanation:

using the square root property of equality to solve  (x - 3)² = -4

we have;

(x - 3)² = -4

Take the square root of both-side

√(x - 3)² = ±√-4

x - 3  =  ±√4  × √-1

Not that square root of -1 is i

x - 3 = ±2i

Add 3 to both-side of the equation

x -3 + 3 = 3 ± 2i

x = 3 ± 2i

Therefore, the solution are 3 ± 2i

Answer 2

The answer is C. 3+-2i

(x-3)$(x-3)^{2} = -4 \sqrt{(x-3)^2} = +- \sqrt{-4 x - 3 = i \sqrt{4} x - 3 = +-2i x = 3 +-2i$