If x + y + Z = 30, 3x + Y-Z = 50, x, y and Z are all nonnegative numbers, the value range of M = 5x + 4Y + 2Z is obtained

If x + y + Z = 30, 3x + Y-Z = 50, x, y and Z are all nonnegative numbers, the value range of M = 5x + 4Y + 2Z is obtained

In this way, we can get the following formula: ① x + y = 40 + X & nbsp; & nbsp; X + y = 40 (x + y = 40, x + y = 40, x + X + y = 40, x + y = 40, x + y = 40, X + y = 40, x + y = 40, x + y = 40, x + y = 40, x + y = 40, x + y = 40, x + y = 40, x + y = 40, x + y = 40, x + X + y = 40, x + y = 40, x + y = 40, x + X + y = 40, x + y = 40, x + X + y = 40, x + X + y = 40, x + X + y = 40, x + X + X + y = 40, x + X + y = 40, x + X + y = 40, x + X + X + y = 40, x + y + X + X + X + X + y = 40, x + X + y = 40; ⑤ The solution is m ≤ 140m ≥ 120m ≤ 130, so 120 ≤ m ≤ 130. Answer: the range of M is 120 ≤ m ≤ 130
If a belongs to R, compare the values of (A-1) 2 and a2-4a + 2
The difference method is used to compare the size
(a-1)^2-(a^2-4a+2)
=a^2-2a+1-a^2+4a-2
=2a-1
① Let 2a-1a ^ 2-4a + 2
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The concept of power of the same base
It's urgent!
There is no formula of addition and subtraction for the same base power, only the same kind of terms can be added and subtracted. Multiply by the same base power, the base number remains unchanged, and add exponentially: A ^ m · a ^ n = a ^ (M + n), such as a ^ 5 · a ^ 2 = a ^ (5 + 2) = a ^ 7, divide by the same base power, the base number remains unchanged, and subtract exponentially: A ^ m △ a ^ n = a ^ (m-n), such as a ^ 5 △ a ^ 2 = a ^ (5-2) = a ^ 3
Given that x, y and Z are nonnegative numbers and satisfy the following conditions: x + y + Z = 30, 3x + Y-Z = 50, find the maximum and minimum of W = 5x + 4Y + 2Z
The sum of the two formulas is: 4x + 2Y = 80, that is: y = 40-2x
Substituting: x + y + Z = 30
The result is: z = X-10
Because x, y, Z are nonnegative,
So, X ≥ 0
y=40-2x≥0
z=x-10≥0
So, 10 ≤ x ≤ 20
So, w = 5x + 4Y + 2Z
=5x+4（40-2x）+2（x-10）
=140-x
Therefore, the value range of W is [120130]
Y + Z = 30-x, Y-Z = 50-3x, y = 40-2x, z = X-10
From X, y, Z are nonnegative numbers, we know x > = 0, Y > = 0, z > = 0, we can get the range of X is 10
Given that the real number a satisfies A2 + 2a-1 = 0, find the value of (1 / A + 1) - (a + 3 / A2-1) * (a2-2a + 1 / A2 + 4A + 3)
1/(a+1)-(a+3)/(a^2-1)*(a^2-2a+1)/a^2+4a+3)
=1/(a+1)-(a+3)/[(a-1)(a+1)]*(a-1)^2/[(a+1)(a+3)]
=1/(a+1)-(a-1)/(a+1)^2
=[(a+1)-(a-1)]/(a+1)^2
=2/(a+1)^2.=2/(a^2+2a+1)
Because a ^ 2 + 2a-1 = 0
So a ^ 2 + 2A = 1
Original formula = 2 / (1 + 1) = 1
Which of the following two powers is the same base power?
A. - x2 and (- x) 3
B. - x2 and x3
C. (- x) 2 and X2
2 and 3 are sum of squares cubes
B
B. - x2 and x3
b. Don't simplify
Given that α is the third quadrant angle, ask if there is such a real number m, so that sin α and cos α are the two roots of the equation 8x2 + 6mx + 2m + 1 = 0 about X. if there is, find out the real number M. if not, explain the reason
Since sin α and cos α are the two roots of the equation 8x2 + 6mx + 2m + 1 = 0 about X, Let f (x) = 8x2 + 6mx + 2m + 1, and its axis of symmetry is x = - 38m. From the above, we know that f (x) has two negative zeros on (- 1,0), ∧ f (0) > 0f (...)
It is known that M = {a-3,2a-1, A2 + 1}, n = {- 2,4a-3,3a-1}. If M = n, then a is a real number=
a^2+1>0
∴①a-3=-2 a=1
M={-2,1,2} N={-2,1,2}
②2a-1=-2 a=-1/2
M = {- 7 / 2, - 2,5 / 4} n = {- 2, - 5, X} rounding off
A=1
On the power of the same base
1. X ^ 3m-n * x ^ 2m-3n * x ^ N-M 2. [- 2] * [- 2] ^ 2 * [- 2] ^ 3 *. * [- 2] ^ 100 3.4 * 2 ^ A * 2 ^ A + 1 = 2 ^ 9, and 2A + B = 8, find the value of a ^ B
One
x^(3m-n)*x^(2m-3n)*x^(n-m)=
=x^(3m-n+2m-3n+n-m)
=x^(4m-3n)
Two
[-2]*[-2]^2*[-2]^3*.*[-2]^100
=[-2]^(1+2+3+.+100)
=[-2]^[(1+100)*100/2]
=[-2]^5050
Three
4*2^a*2^(a+1)=2^9,
4*2^[2+a+(a+1)]=2^9,
That is, 2 + A + (a + 1) = 9,
The solution is a = 3
Substituting 2A + B = 8,
b=8-2a=8-2*3=2
So,
a^b=3^2=9
Given that sin ^ 2 (x) + cos (x) + M = 0 has a real number solution, find the range of M
Sin ^ 2 (x) is the square of sin (x)
The original equation can be transformed into: 1-cos ^ 2 (x) + cosx + M = 0, which is sorted into: cos ^ 2 (x) - cosx-m-1 = 0. The equation can be regarded as a quadratic equation about cosx, that is, T ^ 2-t-m-1 = 0. According to the discriminant of root, we can know that: 1 + 4 (M + 1) is greater than or equal to 0 (1), and the range of T = cosx in the original equation is [- 1,1]
Is sin ^ 2 (x) [sin (x)] ^ 2 or sin [(x)] ^ 2