Arrange the square of the polynomial 2xy-3y + 7x by the ascending power of X, and find out the value of the polynomial x = 1y = - 1 / 2

Arrange the square of the polynomial 2xy-3y + 7x by the ascending power of X, and find out the value of the polynomial x = 1y = - 1 / 2

The square of polynomial 2xy-3y + 7x is arranged as - 3Y & # 178; + 2XY + 7x & # 178 according to the ascending power of X;
The value of this polynomial is - 3Y & # 178; + 2XY + 7x & # 178; = - 3 × (- 1 / 2) &# 178; + 2 × 1 × (- 1 / 2) + 7 × 1 & # 178; = 21 / 4
a. B is the root of the equation 2x ^ 2-3x-1 = 0. Find the absolute value of (a + b)
analysis
(a+b)=-b/a=3/2
(Weida theorem X1 + x2 = - B / a)
x1x2=c/a）
therefore
|a+b|=3/2
If there is no XY term in the quadratic + kxy + X of the algebraic formula 2x and the quadratic + 9 of - 6xy + y, the value of K is obtained
Original formula = 3x & # 178; + (K-6) XY + + Y & # 178; + 9
Without XY, the coefficient is 0
k-6=0
K=6
If the decimal point of a number is moved 3 places to the left, the decimal point of its cube root is moved 1 place to the left
If the decimal point of a number is shifted 3 places to the right, the decimal point of its cube root will be shifted 1 place to the right
If one root of the quadratic equation 2x ^ 2-3x ^ 1-k = 0 is 1, find the other root of the equation
Take x = 1 into 2-3-k = 0, k = - 1, take k = - 1 into the original formula 2x ^ 2-3x + 1 = 0, and then solve the equation X1 = 1, X2 = 1 / 2, so the other root is half
Weida theorem
x1+x2=（-b/a）=1.5
So the other one is 0.5
If the polynomial MX & sup3; + 3nxy & sup2; - 2x & sup3; - XY & sup2; + y contains no cubic term, then 2m + 3N =?
Please give the value of M, N, and give the specific steps!
m-2=0
3n-1=0
M=2
n=1/3
2m+3n=5
Merge congeners
m-2=0,m=2
3n-1=0,n=1/3
2m+3n=5
mx³+3nxy²-2x³-xy²+y
=(m-2)x³+(3n-1)xy²+y
Because the term MX & sup3; + 3nxy & sup2; - 2x & sup3; - XY & sup2; + y contains no cubic term
So m-2 = 0, 3n-1 = 0
So m = 2, n = 1 / 3
So 2m + 3N = 4 + 1 = 5
Simplification:
The original formula = (m-2) x & sup3; + (3n-1) XY & sup2; + y
If there is no cubic term, the coefficient of cubic term is 0,
So m-2 = 0 and 3n-1 = 0
The solution is m = 2 and 3N = 1
So 2m + 3N = 2 × 2 + 1 = 5
If one root of equation 3x ^ 2-2x + a = 0 is 1 / 3 larger than the other root, then the value of a is
Let the two roots be m, N, and M > n
From the Veda theorem
m+n=2/3,mn=a/3
It is also known that M-N = 1 / 3
The solution is m = 1 / 2, n = 1 / 6
So we have Mn = 1 / 12 = A / 3 and get a = 1 / 4
Given that the polynomial MX & sup3; + 3nxy + 2x & sup3; - XY & sup2; + y about X and Y does not contain cubic term, find the value of 2m + 3N
Urgent need
mx³+3nxy²+2x³-xy²+y
=(m+2)x³+(3n-1)xy²+y
The first two are cubic terms
Then their coefficient is 0
So m + 2 = 0, 3n-1 = 0
m=-2,n=1/3
The equation 2x-3 = 4K and x-k / 2 = k-3x of X have the same root?
The root of 2x-3 = 4K is x = (4K + 3) / 2
The root of x-k / 2 = k-3x is x = (K + K / 2) / 4 = 3K / 8
The root is the same, that is (4K + 3) / 2 = 3K / 8
So k = - 12 / 13
2x-3 = 4K, x = (4K + 3) / 2,
5 (x-k) = k-3x, x = 3K / 7,
For the same root, (4K + 3) / 2 = 3K / 7
K = - 21 / 22
To make the polynomial MX & sup3; + 3nxy & sup2; + 2x & sup3; - XY & sup2; + y with respect to the letters X and y not contain cubic terms, find the value of 2m + 3N
MX & sup3; + 3nxy & sup2; + 2x & sup3; - XY & sup2; + y = (M + 2) x & sup3; + (3n-1) XY & sup2; + y does not contain cubic term
So, M + 2 = 0 and 3n-1 = 0, that is, M = - 2, n = one third
2M+3N=-3
The root of the equation 2x + 4K = 16 + 3x about X is greater than 2 but less than 12 when k is chosen
2x-3x=16-4k
x=4k-16
2=