Question

(х-4)(х-5)(х-6)=(х-2)(х-5)(х-6)

Answer 1

(х-4)(х-5)(х-6)-(х-2)(х-5)(х-6)=0 Вынесем (х-5)(х-6)
(х-5)(х-6)(x-4-x+2)=0
-2(х-5)(х-6)=0
x=5,6
Считать х=4,2 корнями-это ошибка:при подстановки в выражения только одно из них обернется в ноль 

Answer 2

To solve this equation, we can start by expanding both sides:

(х-4)(х-5)(х-6) = х³ - 15х² + 86х - 120

(х-2)(х-5)(х-6) = х³ - 13х² + 52х - 60

So the equation becomes:

х³ - 15х² + 86х - 120 = х³ - 13х² + 52х - 60

We can simplify this by bringing all the terms to one side:

-15х² + 34х - 60 = 0

We can factor out -1 to make it easier:

х² - 34/15х + 4 = 0

Now we can use the quadratic formula to solve for x:

х = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = -34/15, and c = 4.

Plugging in these values, we get:

х = (34/15 ± √(34/15)² - 4(1)(4)) / 2(1)

Simplifying this expression, we get:

х = (34/15 ± √(1369/225)) / 2

х = (34/15 ± 37/15) / 2

So the solutions are:

х = 9/5 or х = 2

Therefore, the solutions to the equation (х-4)(х-5)(х-6)=(х-2)(х-5)(х-6) are х = 9/5 and х = 2.