Question

Solve the following quadratic equation by using the definition of a square root and write the solutions in simplified radical form. 3(y-7)² = 24​

Answer 1

y = 7 + 2√2, y = 7 - 2√2

Explanation:

We need to solve for y to find the solutions of the quadratic equation:

3(y-7)^2 = 24

(y-7)^2 = 8

y-7 = ±√8 = ±√(4*2) = ±2√2

y = 7 + 2√2

y = 7 - 2√2

2√2 is the simplified radical form because 4 is the highest factor of 8 that is a perfect square.