Answer:
x = -4 ± 2√3
Step-by-step explanation:
Answer:
x^2 - 2xy + y^2.
Step-by-step explanation:
(x - y)^2
= (x - y)(x - y)
= x(x -y) - y(x - y)
= x^2 - xy - xy + y^2
= x^2 - 2xy + y^2.
Answer:
3x+4
Step-by-step explanation:
f(x) = - x+4
Substitute in x=-3x
f(-3x)= - (-3x) + 4 = 3x+4
The correct answer is d.We have the following system of linear equations:
(I)
![4x+7y=-14](https://tex.z-dn.net/?f=4x%2B7y%3D-14)
(II)
![8x+5y=8](https://tex.z-dn.net/?f=8x%2B5y%3D8)
Let's use the elimination method, then let's multiply the equation (1)
![\times(-2)](https://tex.z-dn.net/?f=%5Ctimes%28-2%29)
and subtracting (I) and (II):
(I)
![-2(4x+7y)=-2(-14)](https://tex.z-dn.net/?f=-2%284x%2B7y%29%3D-2%28-14%29)
∴
![-8x-14y=28](https://tex.z-dn.net/?f=-8x-14y%3D28)
(I)
![-8x-14y=28](https://tex.z-dn.net/?f=-8x-14y%3D28)
(II)
![8x+5y=8](https://tex.z-dn.net/?f=8x%2B5y%3D8)
____________________
(III)
![-9y=36](https://tex.z-dn.net/?f=-9y%3D36)
∴
![y=-4](https://tex.z-dn.net/?f=y%3D-4)
We can find the value of x by substituting y either in (I) or (II). Thus, from (I):
![4x+7(-4)=-14](https://tex.z-dn.net/?f=4x%2B7%28-4%29%3D-14)
∴
![4x-28=-14](https://tex.z-dn.net/?f=4x-28%3D-14)
∴
![4x=14](https://tex.z-dn.net/?f=4x%3D14)
∴
![x=\frac{14}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B14%7D%7B4%7D)
∴
![\boxed{x=\frac{7}{2}}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%3D%5Cfrac%7B7%7D%7B2%7D%7D)
Let's substitute the values of x and y into (I) and (2)
(I)
![4(\frac{7}{2})+7(-4)=14-28=-14](https://tex.z-dn.net/?f=4%28%5Cfrac%7B7%7D%7B2%7D%29%2B7%28-4%29%3D14-28%3D-14)
(II)
![8(\frac{7}{2})+5(-4)=28-20=8](https://tex.z-dn.net/?f=8%28%5Cfrac%7B7%7D%7B2%7D%29%2B5%28-4%29%3D28-20%3D8)
Finally the answer is:
The solution for the given differential equation is lnlxl = ![\frac{-x}{y} +C](https://tex.z-dn.net/?f=%5Cfrac%7B-x%7D%7By%7D%20%2BC)
Given,
![(y^{2} +y^{x} )dx - x^{2} dy =0](https://tex.z-dn.net/?f=%28y%5E%7B2%7D%20%2By%5E%7Bx%7D%20%29dx%20-%20x%5E%7B2%7D%20dy%20%3D0)
Here,
x = vy, dx = vdy + ydv
y = ux, dy = udx + xdu
Then,
![((ux)^{2} +(ux)x)dx-x^{2} (udx+xdu)=0\\=u^{2} x^{2} dx+ux^{2} dx-x^{2} udx-x^{3} du=0\\=u^{2} x^{2} dx=x^{3} du\\=\frac{x^{2} }{x^{3} } dx=\frac{1}{u^{2} } du](https://tex.z-dn.net/?f=%28%28ux%29%5E%7B2%7D%20%2B%28ux%29x%29dx-x%5E%7B2%7D%20%28udx%2Bxdu%29%3D0%5C%5C%3Du%5E%7B2%7D%20x%5E%7B2%7D%20dx%2Bux%5E%7B2%7D%20dx-x%5E%7B2%7D%20udx-x%5E%7B3%7D%20du%3D0%5C%5C%3Du%5E%7B2%7D%20x%5E%7B2%7D%20dx%3Dx%5E%7B3%7D%20du%5C%5C%3D%5Cfrac%7Bx%5E%7B2%7D%20%7D%7Bx%5E%7B3%7D%20%7D%20dx%3D%5Cfrac%7B1%7D%7Bu%5E%7B2%7D%20%7D%20du)
Now,
![\int\limits^a_b {\frac{1}{x} } \, dx =\int\limits^a_b {u^{-2} } \, du](https://tex.z-dn.net/?f=%5Cint%5Climits%5Ea_b%20%7B%5Cfrac%7B1%7D%7Bx%7D%20%7D%20%5C%2C%20dx%20%3D%5Cint%5Climits%5Ea_b%20%7Bu%5E%7B-2%7D%20%7D%20%5C%2C%20du)
l
l
l![=\frac{u^{-1} }{(-1)} +C](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bu%5E%7B-1%7D%20%7D%7B%28-1%29%7D%20%2BC)
l
l
l![=\frac{-1}{u} +C](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-1%7D%7Bu%7D%20%2BC)
y = ux
u = ![\frac{y}{x}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Bx%7D)
That is l
l
l ![=\frac{-x}{y} +C](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-x%7D%7By%7D%20%2BC)
Learn more about differential equation here: brainly.com/question/21852102
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