Question

(3y-1)^2-(3y-2)^2=0 Решите уравнение

Answer 1

9y^2-6y+1-(9y^2-12y+4)=0

9y^2-6y+1-9y^2+12y-4=0

6y-3=0

6y=3

y=1/2

Answer 2

To solve the equation, let's first simplify it by applying the difference of squares formula, which states that (a^2 - b^2) = (a + b)(a - b):

(3y - 1)^2 - (3y - 2)^2 = 0

Using the difference of squares formula:

[(3y - 1) + (3y - 2)][(3y - 1) - (3y - 2)] = 0

Now, simplify further:

[6y - 3 + 1][6y - 3 - 1] = 0

(6y - 2)(6y - 4) = 0

Now, set each factor to zero and solve for y:

1. 6y - 2 = 0 6y = 2 y = 2/6 y = 1/3

2. 6y - 4 = 0 6y = 4 y = 4/6 y = 2/3

So, the solutions to the equation are y = 1/3 and y = 2/3.