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Let m and n be positive integers, 3M + 2n = 45. If the greatest common divisor of M and N is 3, find m and n
m. The greatest common divisor of n is 3
Let m = 3S, n = 3T
Substitute 3M + 2n = 45 to get
3s+2t=15
It's tempting
s=1,t=6,m=3,n=18
S = 3, t = 3, M = 9, n = 9 (rounding off)
So m = 3, n = 18
Given a + B = 1, ab = 316, find the value of the algebraic formula a3b-2a2b2 + AB3
A3b-2a2b2 + AB3 = AB (a2-2ab2 + B2) = AB (a-b) 2 = AB [(a + b) 2-4ab] substituting a + B = 1, ab = 316, the original formula is 316 × [12-4 × 316] = 364
Given a + B = 2, ab = 3 / 16, then the value of a ^ 3 + 2A ^ 2B ^ 2 + AB ^ 3 is
a^3+2a^
1. If point a (a + 1,3) and point B (- 2,2-b) are symmetric about the origin, find the square root of 2A + 2B
2. Linear function y = (2m + 4) x + M-6
(1) Through the origin, find M
(2) But in the fourth quadrant, I want to find the range of M
Ask for the guidance of the great God! The process! Tonight!
1.a+1=2 a=1 2-b=-3 b=5
2a+2b=12
The square root is 2 and the sign is 3
If 2 (1) passes through the origin, then M-6 = 0
m=6
(2) But in the fourth quadrant, 2m + 4 > 0, M-6 > 0
∴m＞6
In rectangular coordinate system, given that point a (2a-b, a + b) and point B (a-6, B-9) are symmetrical with respect to the origin of coordinates, find the values of a and B, and write out the coordinates of two points
In Cartesian coordinate system, we know that point a (2a-b, a + b) and point B (a-6, B-9) are symmetric about the origin of coordinate
xA+xB=0,2a-b+a-6=0,3a-b=6.(1)
yA+yB=0,a+b+b-9=0,a=9-2b.(2)
(2) Substituting (1), we get
3*(9-2b)-b=6
a=3,b=3
A (3,6), point B (- 3, - 6)
In the rectangular coordinate system, a (2a, A-B + 1), B (B, a + 1) are symmetrical about the origin. 1. Calculate the value of a, B. 2. Calculate the length of line ab
Because a and B are symmetrical about the origin, 2A = - B; A-B + 1 = - (a + 1)
A = - 1 / 2; b = 1
So a (- 1, - 1 / 2) B (1,1 / 2), the distance between two points is root five
In the rectangular coordinate system, given that the points a (2a-b, a + b), B (a-6, B-9) are symmetrical about the origin of coordinates, find the values of a and B, and write out the coordinates of these two points
On the symmetry of coordinate origin
X and y are opposite numbers, respectively
2a-b+a-6=0
a+b+b-9=0
therefore
b=3a-6
Then a + 6a-12-9 = 0
a=3
b=3a-6=3
A(3,6)
B(-3,-6)
In the rectangular coordinate system, the coordinates of point a are (- 3,4), and the coordinates of point D are (0,5). Point B and point a are symmetrical about the X axis, and point C and point a are symmetrical about the origin
Finding the area of quadrilateral ABCD
Because points B and a are symmetric about the X axis, B (- 3, - 4)
Because point C and point a are symmetric about the origin, C (3, - 4)
So s quadrilateral ABCD = 48
In Cartesian coordinate system, given a (- 3,4) d (0,5), point B and point a are axisymmetric about X axis, and point C and point a are centrosymmetric about origin O. find s □ ABCD
According to the meaning of the title, B (- 3, - 4) C (3, - 4) so s □ ABCD = 3 × 8 + 1 / 2 × 3 × 9 + 1 / 2 × 3 × 1 = 24 + 13.5 + 1.5 = 39
In the rectangular coordinate system, the point P (- 2,3) is symmetric with respect to the origin, and the point coordinates are ()
A（2,—3） B（2,3） C（—2,—3） D（3,—2）
Choose C
The rule is
Symmetry with origin
The x-axis does not change, and the y-axis is the opposite of the original number
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