Question

(x-3)^2=2x-3...............

Answer 1

(х-3)²=2х-3

х²-6х+9-2х+3=0

х²-8х+12=0

D/4 = 4²-12=4 ( ±2² )

х1=4+2=6

х2=4-2=2

Answer 2

To solve the equation $(x - 3)^2 = 2x - 3$, you can follow these steps:

Step 1: Expand the left side of the equation: $(x - 3)^2 = x^2 - 6x + 9$

Step 2: Rewrite the equation with the expanded expression: $x^2 - 6x + 9 = 2x - 3$

Step 3: Move all terms to one side of the equation to set it equal to zero: $x^2 - 8x + 12 = 0$

Step 4: Factor the quadratic expression: $(x - 2)(x - 6) = 0$

Step 5: Set each factor equal to zero and solve for x: $x - 2 = 0 \implies x = 2$ or $x - 6 = 0 \implies x = 6$

So, the solutions for the equation $(x - 3)^2 = 2x - 3$ are $x = 2$ and $x = 6$.