Question

Which values are approximate solutions (k 12)^2= 97

Answer 1

To find the approximate solutions for the equation (k + 12)^2 = 97, we take the square root of both sides to obtain two separate equations and solve for k. The two approximate solutions for k after calculation are -2.151 and -21.849.

Step-by-step explanation:

The given equation is (k + 12)^2 = 97. To find the approximate solutions for this equation, we first need to solve for k. We start by taking the square root of both sides of the equation to get k + 12 = ±97 (which includes both the positive and negative square roots). This gives us two equations to solve:

1. k + 12 = √97
2. k + 12 = -√97

Solving each of these equations for k:

1. k = √97 - 12
2. k = -√97 - 12

Using a calculator, we find √97 is approximately 9.849, thus:

1. k ≈ 9.849 - 12
2. k ≈ -9.849 - 12

This results in two approximate solutions for k:

• k ≈ -2.151
• k ≈ -21.849