Given that X and y satisfy X & # 178; + Y & # 178; + 5 / 4 = x-2y, what is the value of 2x + y?

Given that X and y satisfy X & # 178; + Y & # 178; + 5 / 4 = x-2y, what is the value of 2x + y?

x²+y²+5/4=x-2y
x²-x+y²+2y+5/4=0
(x²-x+1/4)+(y²+2y+1)=0
(x-1/2)²+(y+1)²=0
∴x-1/2=0,y+1=0
∴x=1/2,y=-1
∴2x+y
=2*1/2+(-1)
=1-1
=0

Cross multiplied. Given (2x & # 178; + 2Y & # 178;) (X & # 178; - 2 + Y & # 178;) - 16 = 0, find the value of the fourth power of X + the fourth power of Y + 2x & # 178; Y & # 178;)

(x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\letx and 178; + y and 178;) = 8 let X and 178; + y and 178; = t (t

Given x = 1 / 2, find the value of X & # 178; - 1 / X & # 178; - 2x + 1 + X & # 178; - 2x / X-2

x=1/2
(x²-1)/(x²-2x+1)+(x²-2x)/(x-2)
=(x-1)(x+1)/(x-1)²+(x-2)x/(x-2)
=(x+1)/(x-1)+x
=[3/2]/[1/2]+1/2
=3+1/2
=7/2

Given X & # 178; - X-1 = 0, find the value of X & # 179; - 2x-1

Solution
x²-x-1=0
x²-x=1
∴x³-2x-1
=x(x²-x)-x²-1
=x-x²-1
=-(x²-x)-1
=-1-1
=-2

How many digits did Xiaojun count from 1 to 100

9: 1;
10-19:11
20-99: 8
100:1
21 in total

x: Y = 1:3, Y: z = 1:4, and x-2y + 3Z = 62, find the value of the polynomial XY YZ = XZ
It's a plus sign. Sorry, wrong number

x: Y = 1:3, Y: z = 1:4, we can get y = 3x, z = 4x, y = 12x
If x-2y + 3Z = 62, we can get x-6x + 36x = 62, so x = 2
Then y = 6, z = 12x = 24
If it is xy-yz-xz, then it is 2x6-6x24-2x24 = - 180
If it is XY YZ + XZ, then it is 2x6-6x24 + 2X24 = - 84

1, 7, 19, 37, 61... What's the nth number
Write the general formula

The difference is 6N
General formula = 1 + 6 * (1 + 2 +... N-1) = 1 + 6 * (n-1) n / 2 = 3N ^ 2-3n + 1

Finding the general solution of the equation XY '' = y'ln (y '/ x)

Let y = y 'reduce the order
Y'=(Y/x)ln(Y/x)
This is a homogeneous equation of first order
Let Y / x = u, so y = UX, y '= u + X (DU / DX)
lnu=C1x+1
Y=xe^(C1x+1)
So y = [(c1x-1) e ^ (c1x + 1)] / C1 & # 178; - C2

What does forest rely on to conserve water and prevent soil erosion

In fact, not only can forests conserve water and prevent soil erosion, but also green vegetation can. The principle is photosynthesis, respiration and leaf evaporation of plants

Any seven unequal natural numbers, at least two of which are multiples of 6. Why

The remainder of a natural number divided by 6 may be 0, 1, 2, 3, 4, 5, a total of six possibilities
According to the drawer principle, there must be two of any seven natural numbers divided by 6 with the same remainder, then the difference between the two numbers is a multiple of 6