Question

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

Answer 1

y = 9.75

Explanation:

(4y - 3)2 = 72

Opening the brackets;

8y - 6 = 72

8y = 72 + 6 = 78

y = 78 ÷ 8 = 9.75

Answer 2

`y = (3+6√(2))/(4)\text{ and } y = (3-6√(2))/(4)`

Explanation:

Given quadratic equation,

`(4y-3)^2=72`

`\implies 4y - 3 = \pm √(72)` ( Taking root on both sides )

`4y=3 \pm 6√(2)` ( Additive property of equality ),

`y = (3 \pm 6√(2))/(4)` ( Division property of equality )

`\implies y = (3+6√(2))/(4)\text{ or }y =(3-6√(2))/(4)`

Hence, the solution of the given equation is,

`\implies y = (3+6√(2))/(4)\text{ and }y =(3-6√(2))/(4)`