Question

(3x−2)^2−(x−11)^2=0.

Answer 1

$(3x-2)^{2} -(x-11)^{2}=0\\\\(3x-2-x+11)(3x-2+x-11)=0\\\\(2x+9)(4x-13)=0\\\\1)2x+9=0\\\\2x=-9\\\\x_{1}=-4,5\\\\2)4x-13=0\\\\4x=13\\\\x_{2}=3,25\\\\Otvet:\boxed{-4,5 \ ; \ 3,25}$

Answer 2

Ответ:

(3x−2)^2−(x−11)^2=0.

8x^+10x-117=0

(2x+9) (4x-13)=0

2x+9=0 or 4x-13=0

2x= -9 or 4x-13=0

x= - $\frac{9}{2}$ or 4x-13=0

x= - $\frac{9}{2}$ or 4x=13

x= - $\frac{9}{2}$    x=$\frac{13}{4}$

Answer 3

To solve the equation (3x - 2)^2 - (x - 11)^2 = 0, you can use the difference of squares identity, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = (3x - 2) and b = (x - 11).

So, you can rewrite the equation as follows:

(3x - 2 + x - 11)(3x - 2 - x + 11) = 0

Now, simplify both factors:

(4x - 13)(2x + 9) = 0

Now, set each factor equal to 0 and solve for x:

1. 4x - 13 = 0 4x = 13 x = 13/4

2. 2x + 9 = 0 2x = -9 x = -9/2

So, the solutions for the equation (3x - 2)^2 - (x - 11)^2 = 0 are x = 13/4 and x = -9/2.