If the sum of a two digit number, a ten digit number and a single digit number is 9, and the product of these two digits is equal to twice the sum of their two digits, calculate these two digits

Let ten digits be X
X*(9-X）=9*2
X²-9X+18=0
(x-6)(x-3)=0
x1=6 x2=3
Two digit = 36 or 63

For a two digit number, the ten digit number is three times larger than the single digit number, and the product of the ten digit number and the single digit number is equal to two seventh of the two digit number?

Single digit x ten digit x + 3
x(x+3)=[10(x+3)+x)*2/7
7x^2+21x=22x+60
7x^2-x-60=0
(7x+20)(x-3)=0
X = - 20 / 7 (rounding off)
x=3
This two digit number is 63

A two digit number is equal to three times the number product of its digits. The number of ten digits is 2 less than the number of one digit. What are the two digits?

Let the number in ten be x and the number in one be y
Then (10x + y) / xy = 3, x + 2 = y
The simultaneous two formulas can be obtained as X1 = - 1 / 3, and X2 = 2
Y=X+2=4
So this number is
twenty-four
Experience meets the requirements of the title

In quadratic function y = 2x2 + PX + Q, if P-Q = 0, then its image must pass through point () A. (- 1,2) B. (1,2) C. (- 1, - 2)

Select a, and substitute x = - 1, y = 2 into function verification

If the minimum value of quadratic function y = x & # 178; + PX + Q is 4, when x = 2, y = 5, then the values of P and Q are?

The quadratic functions are sorted out as follows: y = x & # 178; + PX + P & # 178; + 4-P & # 178; + q = (x + P / 2) &# 178; + Q-P & # 178; + 4. When x = - P / 2, y reaches the minimum value of 4. Therefore, Q-P & # 178; / 4 = 4, q = P & # 178; / 4 + 4 (in duplicate) brings x = 2, y = 5, 5 = 4 + 2p + Q, 2p + q = 1 (in duplicate), and then the duplicate and the binary are simultaneous

(1) If the minimum value of quadratic function y = x ^ 2 + PX + Q is 4, when x = 2, y = 5, the value of P, q is
(2) Given that the vertex of parabola y = - x ^ 2 + 4x + A and y = (x-a + b) ^ 2 + 5A + B are the same, find the value of a and B (process)
(3) For quadratic function y = ax ^ 2 + BX + C, if B is not equal to 0 and C = 0, then the vertex of y = ax ^ 2 + BX is__ The axis of symmetry is_ Its image must have passed through_____

1. According to the minimum value of 4, Q equals 4 and P equals 1.5, so p = - 1.5, q = 4
2. It's too complicated for me to say that you need to do the calculation. Expand the second calculation y = (x-a + b) ^ 2 + 5A + B to get a quadratic term, a quadratic term and a constant term. The vertex wants to be the same, so the formula of the constant term is equal to a, the coefficient of the first term is equal to 4, and the system of the quadratic term is equal to 1!
3. Standard quadratic trinomial, go to algebra book
(- B / 2a, sqrt [4ac-b ^ 2] / 4A), the axis of symmetry x = - B / 2a, passing through 0,0

It is known that when x = 5, the quadratic function y = x & sup 2; + PX + Q has a minimum value of - 2
Find the vertex coordinates and symmetry axis equation of the image of the function y = & sup2; + (Q-15) X-P and the value range of X when y > = 3
Find the vertex coordinates and symmetry axis equation of the image of the function y = x & sup2; + (Q-15) X-P, and the value range of X when y > = 3.

Y = x & sup2; + PX + q = (x + P / 2) 2 + q-p2 / 4, that is, when x = - P / 2, y = q-p2 / 4 and - P / 2 = 5, q-p2 / 4 = - 2 leads to P = - 10, q = 23y = x & sup2; + (Q-15) X-P = x & sup2; + 8x + 10 = (x + 4) 2-6, that is, vertex coordinates (- 4, - 6), symmetry axis equation x = - 4, when y > = 3, then x & sup2; + 8x + 10 > = 3 leads to

It is known that when x = 5, the quadratic function y = x ^ 2 + PX + Q has a minimum value of - 2
(1) Finding the value of P and Q
(2) Write out the symmetry axis equation and vertex coordinates of the function y = x ^ 2 + (Q-15) X-P and the value range of X when y ≥ 3

It is known that when x = 5, the quadratic function y = x ^ 2 + PX + Q has a minimum value of - 2, then - P / 2 = 5,25 + 5p + q = - 2 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; the solution is p = - 10, q = 23,2. From (1), the equation of symmetry axis of y = x & # 178; + 8x + 10 is x = - 4, vertex coordinates (- 4, - 6) x & # 178; + 8x + 10 ≥ 3, that is, X & # 178; + 8x + 7 ≥ 0 (x + 1) (x + 7) ≥ 0, so: X ≤ & nbsp; - 7 or X ≥ - 1

If the square of X - Px + q = (x + a) * (x + b)
.
So p equals

-p=a+b p=-a-b

If the sum of a two digit number, a ten digit number and a single digit number is 9, and the product of these two digits is equal to twice the sum of their two digits, calculate these two digits