Let's start by expanding the given equations:
Expanding (2x-3)^2(2x-3)^2 = (2x-3)(2x-3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9
Expanding (2x+5)(2x-5)(2x+5)(2x-5) = 4x^2 - 10x + 10x - 25 = 4x^2 - 25
Expanding (2x+3)^2(2x+3)^2 = (2x+3)(2x+3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9
Now, substituting these expanded forms into the given equations:
(2x-3)^2 - (2x+5)(2x-5) = 24x^2 - 12x + 9 - (4x^2 - 25) = 24x^2 - 12x + 9 - 4x^2 + 25 = 2-12x + 34 = 2-12x = -1x = 11/12
(2x-5)(2x+5) - (2x+3)^2 = -(4x^2 - 25) - (4x^2 + 12x + 9) = -4x^2 - 25 - 4x^2 - 12x - 9 = --12x - 34 = --12x = 3x = -33/12
Therefore, the solutions to the given equations are x = 11/12 and x = -33/12.
Let's start by expanding the given equations:
Expanding (2x-3)^2
(2x-3)^2 = (2x-3)(2x-3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9
Expanding (2x+5)(2x-5)
(2x+5)(2x-5) = 4x^2 - 10x + 10x - 25 = 4x^2 - 25
Expanding (2x+3)^2
(2x+3)^2 = (2x+3)(2x+3) = 4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9
Now, substituting these expanded forms into the given equations:
(2x-3)^2 - (2x+5)(2x-5) = 2
4x^2 - 12x + 9 - (4x^2 - 25) = 2
4x^2 - 12x + 9 - 4x^2 + 25 = 2
-12x + 34 = 2
-12x = -1
x = 11/12
(2x-5)(2x+5) - (2x+3)^2 = -
(4x^2 - 25) - (4x^2 + 12x + 9) = -
4x^2 - 25 - 4x^2 - 12x - 9 = -
-12x - 34 = -
-12x = 3
x = -33/12
Therefore, the solutions to the given equations are x = 11/12 and x = -33/12.