Question

Which is the solution of the quadratic equation (4y - 3)² = 72?

A. y= 3 +6√2/4 and y = 3-6√2/4
B. y = 3 +6V2/4 and y =-3-6√2/4
C. y= 9√2/4 and y= -3√2/4
D. y = 9√7/4 and y = 3√2/4

Answer 1

The solution to the quadratic equation (4y - 3)² = 72 is found by taking the square root of both sides, simplifying, and then isolating y, which gives y = (3 + 6√2) / 4 and y = (3 - 6√2) / 4, corresponding to option A.

Step-by-step explanation:

The student is asking for the solution to the quadratic equation (4y - 3)² = 72. To solve quadratic equations, one method involves expanding the squared term, setting the expression equal to zero, and then applying the quadratic formula, which is -b ± √(b² - 4ac) / (2a). But in this case, we can simplify the equation by taking the square root of both sides before isolating the variable y.

Let's solve the equation step by step:

1. Take the square root of both sides of the equation to get 4y - 3 = ±√72.
2. Recognizing that √72 can be simplified to 6√2, the equation becomes 4y - 3 = ±6√2.
3. Add 3 to both sides to isolate the term with y: 4y = 3 ± 6√2.
4. Finally, divide both sides by 4 to solve for y, yielding y = (3 ± 6√2) / 4.

So, the solutions are y = (3 + 6√2) / 4 and y = (3 - 6√2) / 4, which corresponds to option A.