If both equations x2-11x + 30 + a = 0 are greater than 5, then the value range of real number a is______ ．

If both equations x2-11x + 30 + a = 0 are greater than 5, then the value range of real number a is______ ．

Let two equations x2-11x + 30 + a = 0 be x1, X2, because both of them are greater than 5, so there are (x1-5) + (x2-5) > 0 and (x1-5) (x2-5) > 0, that is, X1 + x2-10 > 0 and x1 ·x2-5 (x1 + x2) + 25 > 0. From WIDA's theorem, we can get: X1 + x2 = 11, x1x2 = 30 + A,  30 + A-55 + 25 > 0, the solution is a > 0, and ∧ = (- 11) 2-4 (30 + a) ≥ 0, the solution is a ≤ 14, so the value range of real number a is: (0, 14] The answer is: (0, 14]

Given that the equation 2x square - [M + 1] x + M = 0 has a positive root and a negative root, then the value range of real number m is?

2X & # 178; - (M + 1) x + M = 0 has a positive root and a negative root
∴ x1*x2 = m/2 < 0
△ = (m+1)² - 8m > 0
That is, when M 0
Obviously, it is true at M 0
The value range of real number m is m < 0

Proof: equation 2x2 + 3 (m-1) x + m2-4m-7 = 0, for any real number m, there are always two unequal real roots

For any real number m, (M + 7) 2 ≥ 0, the original equation has two unequal real roots. Therefore, for any real number m, the equation 2x2 + 3 (m-1) x + m2-4m-7 = 0 will always have two unequal real roots

If one third of the number a is equal to one fourth of the number B, then the number a is equal to one fourth of the number B

(1 / 3) * number a = (1 / 4) * number B
Number A: number b = (1 / 4): (1 / 3) = 3:4

For a right triangle, if one right edge is increased by 5 cm and the area is increased by 2 square cm, if the other right edge is also increased by 4 cm and the area is increased by 18 square cm, the area of the original triangle can be calculated?
No equation solution, formula calculation, explanation,)

2 × 2 △ 5 = 0.8 cm (another right angle side)
18 × 2 △ 4 = 9cm (the first right angle side)
Original triangle area = 9 × 0.8 △ 2 = 3.6 square centimeter

3 / 4 of a is equal to 4 / 5 of B. the ratio of a to B is ()

3 / 4 of a is equal to 4 / 5 of B. the ratio of a to B is (16:15)

Let the augmented matrix B = (a | b) of the system AX = b be a square matrix of order m, and | B | is not equal to 0, then what is the solution of the system
Ask for advice,

|If B | is not equal to 0, then R (b) = M
And a matrix is m * (m-1) matrix, so r (a)

It takes 6 hours for Party A and 5 hours for Party B to process a batch of parts. What is the efficiency ratio of Party A and Party B?
Understand

First of all, you should know what is production efficiency. Production efficiency is the number of parts produced per unit time. Therefore, the work efficiency ratio of Party A and Party B is the inverse ratio of time, which is 5:6

If (5x + y) (7x + 10Y) = 1 / 2, then x / Y=______ If x + 1 / x = 3, then x ^ 2 + 1 / x ^ 2

Unless the condition is (5x + y) / (7x + 10Y) = 1 / 2, then x / y = 3 / 8
X + 1 / x = 3, then x ^ 2 + 1 / x ^ 2 = (x + 1 / x) ^ 2-2 = 7

There are 7 tons of grain in warehouse A and 60 tons in warehouse B. how many tons of grain will be taken out from warehouse A to warehouse B so that the ratio of grain storage tons in warehouse A and warehouse B is 5:8

There are 70 tons of grain in warehouse a,
The total number remains unchanged
Now a has: (70 + 60) / (5 + 8) × 5 = 50 tons
Take out from a: 70-50 = 20 tons