Question

(x+2 y)^2-(x-2 y)^2/x при x=корень из 8 y=-7

Answer 1

$\frac{(x+2y)^2-(x-2y)^2}{x}=\frac{(x+2y-x+2y)(x+2y+x-2y)}{x}= \frac{4y*2x}{x}=8y$
Подставим значение "y" в наше выражение:
8*(-7)=-56
Ответ: -56

Answer 2

To find the value of the expression $\frac{(x+2y)^2 - (x-2y)^2}{x}$ when $x = \sqrt{8}$ and $y = -7$, we can simply substitute these values into the expression.

Let's proceed with the calculations step-by-step:

1. Substitute the values of $x$ and $y$ into the expression: $\frac{(\sqrt{8} + 2(-7))^2 - (\sqrt{8} - 2(-7))^2}{\sqrt{8}}$

2. Simplify the terms inside the parentheses: $\frac{(\sqrt{8} - 14)^2 - (\sqrt{8} + 14)^2}{\sqrt{8}}$

3. Simplify the squared terms: $\frac{(\sqrt{8} - 14)(\sqrt{8} - 14) - (\sqrt{8} + 14)(\sqrt{8} + 14)}{\sqrt{8}}$

4. Expand the squared terms: $\frac{8 - 28\sqrt{8} + 196 - (8 + 28\sqrt{8} + 196)}{\sqrt{8}}$

5. Simplify further: $\frac{-28\sqrt{8} + 196 - 28\sqrt{8} - 196}{\sqrt{8}}$

6. Combine like terms: $\frac{-56\sqrt{8}}{\sqrt{8}}$

7. Cancel out $\sqrt{8}$ from the numerator and denominator: $-56$

So, the value of the expression $\frac{(x+2y)^2 - (x-2y)^2}{x}$ when $x = \sqrt{8}$ and $y = -7$ is $-56$.