Question

(4у - З)2 - (2у + 5)2 = 0

Answer 1

(4y-3)2-(2y+5)2=0
8y-6-4y+10=0
8y-4y=6-10
4y=-4
y=-1

Answer 2

To solve the equation (4у - З)² - (2у + 5)² = 0, we can use the difference of squares formula, which states that a² - b² = (a + b)(a - b).

Let's apply this formula to the equation:

(4у - З + 2у + 5)(4у - З - 2у - 5) = 0

Simplifying further:

(6у + 5)(2у - 10) = 0

Now we have two factors, and either of them can be equal to zero for the whole equation to be satisfied.

Setting the first factor equal to zero:

6у + 5 = 0 6у = -5 у = -5/6

Setting the second factor equal to zero:

2у - 10 = 0 2у = 10 у = 10/2 у = 5

Therefore, the solutions to the equation (4у - З)² - (2у + 5)² = 0 are у = -5/6 and у = 5.