Question

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

a) (y = 3 + √72/2, quad y = 3 - √72/2)

b) (y = 3 - √72/2, quad y = 3 + √72/2)

c) (y = 9/2, quad y = -3/2)

d) (y = -3/2, quad y = 9/2)

Answer 1

To solve the quadratic equation ((4y - 3)^2 = 72), we can take the square root of both sides and simplify the equation to obtain the solutions. The correct solution is option a) (y = 3 + √72/2, quad y = 3 - √72/2).

Step-by-step explanation:

The quadratic equation given is ((4y - 3)^2 = 72).

To solve this equation, we can start by taking the square root of both sides to eliminate the square. This gives us the equation (4y - 3) = ±√72.

Simplifying further, we have 4y - 3 = ±6√2. Now we can add 3 to both sides, giving us 4y = 3 ± 6√2. Finally, we divide both sides by 4 to solve for y, obtaining the solutions (y = 3 + 6√2/4) and (y = 3 - 6√2/4).

Therefore, the correct solution of the quadratic equation is option a) (y = 3 + √72/2, quad y = 3 - √72/2).