Question

(y-2)(y+3)-(y-2)2=5. y=??​

Answer 1

Ответ:

(y-2)(y+3)-(y-2)²=(y²+3y-2y-6)-(y²-4y+4)=y²+3y-2y-6-y²+4y-4=5y-10=0

5y=10

y=2

Answer 2

To solve for y in the equation $(y-2)(y+3)-(y-2)^2=5$, you can follow these steps:

1. Expand both sides of the equation: $(y-2)(y+3)-(y-2)^2=5$

   Expand the left side by multiplying $(y-2)$ with $(y+3)$ and $(y-2)$ with itself: $(y^2 + 3y - 2y - 6) - (y^2 - 4y + 4) = 5$

2. Simplify and combine like terms on the left side of the equation: $(y^2 + y - 6) - (y^2 - 4y + 4) = 5$

   Now, distribute the negative sign to the terms inside the parentheses on the left side: $y^2 + y - 6 - y^2 + 4y - 4 = 5$

3. Simplify further by canceling out like terms: $y^2$ and $-y^2$ cancel each other out, and $y$ and $4y$ combine to $5y$: $y - 6 + 4y - 4 = 5$

4. Combine like terms on the left side: $5y - 10 = 5$

5. Add 10 to both sides to isolate the term with $y$: $5y = 5 + 10$

6. Simplify: $5y = 15$

7. Finally, divide both sides by 5 to solve for $y$: $y = \frac{15}{5}$

8. Simplify the fraction: $y = 3$

So, the solution to the equation $(y-2)(y+3)-(y-2)^2=5$ is $y = 3$.