Question

(x-3)(x-4)(x-5)=(x-2)(x-4)(x-5)

Answer 1

(х-3)(х-4)(х-5)=(х-2)(х-4)(х-5)
(х-3)(х-4)(х-5)-(х-2)(х-4)(х-5)=0
(x-4)(x-5)*(x-3-x+2)=0
-1(x-4)(x-5)=0
(x-4)(x-5)=0
x=4
x=5

Answer 2

To solve the equation (x-3)(x-4)(x-5) = (x-2)(x-4)(x-5), we can start by simplifying both sides of the equation. Let's expand the expressions:

Left side: (x-3)(x-4)(x-5) = (x^2 - 7x + 12)(x-5) = x^3 - 5x^2 - 7x^2 + 35x + 12x - 60 = x^3 - 12x^2 + 47x - 60.

Right side: (x-2)(x-4)(x-5) = (x^2 - 7x + 10)(x-5) = x^3 - 5x^2 - 7x^2 + 35x + 10x - 50 = x^3 - 12x^2 + 45x - 50.

Now, the equation becomes:

x^3 - 12x^2 + 47x - 60 = x^3 - 12x^2 + 45x - 50.

To solve for x, we can now cancel out the common terms on both sides, which are the x^3 and the -12x^2:

x^3 - 12x^2 + 47x - 60 - (x^3 - 12x^2 + 45x - 50) = 0.

Simplifying further:

x^3 - 12x^2 + 47x - 60 - x^3 + 12x^2 - 45x + 50 = 0.

Now, the x^3 and -x^3 terms cancel out, and the -12x^2 and +12x^2 terms also cancel out:

47x - 60 - 45x + 50 = 0.

Combine like terms:

2x - 10 = 0.

Now, isolate x by moving the constant term to the other side of the equation:

2x = 10.

Finally, divide both sides by 2 to solve for x:

x = 10/2.

Therefore, the solution to the equation is:

x = 5.