Question

Найдите корень уравнения (х-5)^2=(х-7)^2

Answer 1

(x-5)²=(x-7)²

Решение 1.
x²-10x+25=x²-14x+49
-10x+14x=49-25
4x=24
x=6

Решение 2.
Т.к. x-5≠x-7, а квадраты этих выражений равны, то это значит, что сами выражения имеют разные знаки. Т.е.,
x - 5 = 7 - x ⇔ 2x = 12 ⇔ x=6

Answer 2

I can help you with your math problem. The equation you have given is $(x-5)^2=(x-7)^2$. To find the root of this equation, we need to solve for $x$. Here are the steps:

- Expand the squares on both sides: $x^2-10x+25=x^2-14x+49$. - Subtract $x^2$ from both sides: $-10x+25=-14x+49$. - Add $14x$ to both sides: $4x+25=49$. - Subtract $25$ from both sides: $4x=24$. - Divide both sides by $4$: $x=6$.

Therefore, the root of the equation is $x=6$. You can check this by plugging in the value of $x$ into the original equation and verifying that both sides are equal.

I hope this helps you understand how to solve quadratic equations. If you need more help, you can use this online calculator that shows you the steps and the answer. You can also read this blog post that explains how to solve quadratic equations in general.

: [Online calculator for quadratic equations](https://ru.symbolab.com/solver/roots-calculator) : [High School Math Solutions – Quadratic Equations Calculator, Part 1](https://uchi.ru/otvety/questions/naydite-koren-uravnenie-7-x-5-2)