Mathematics 3rd Grade, Finding Solutions, Question 15

Question 15. a（a,b）

then b(-a,b).

b is on y=x+3, so b=-a+3, i.e. a+b=3a is on y=1 (2x), so b=1 2a, i.e., ab=1 2a b+b a=(a 2+b 2) (ab)=((a+b) 2-2ab) ab=16

Guo Dunyun: Substituting the coordinate value of a(a,b) into the inverse function y=1 2x obtains, b=1 2a (1).

The two points a and b are symmetrical with respect to the y axis, then the coordinates of point b are b( a,b), and the linear function y=x+3 is substituted for the linear function, b= a+3 (2).

Synaptic from (1) and (2), 1 2a = a+3

2a²－6a+1=0，a1=3+（1/2）√7，a2=3－（1/2）√7；

b1=－a+3=－[3+（1/2）√7]+3=－（1/2）√7，b2=－a+3=－[3－（1/2）√7]+3=（1/2）√7。

Substituting a1=3+(1 2) 7 and b1 = (1 2) 7) into b a+a b, b a+a b = [(1 2) 7] [ 3+(1 2) 7]+[3+(1 2) 7] [ 1 2) 7].

Connecting AC and EF is the mid-vertical line of AB and CD.

ad = ac

ABCD is square.

ad = cd

ACD is an equilateral triangle.

adc =60°，∠ada=30

DG deuces the ADA

adg=15°

I know fb 1 and df 2, so we can find db

AB can be found using the Pythagorean theorem from db and ad.

x/(x-1) +m/[-(x-1)] 2=0x/(x-1) -m/(x-1) -2(x-1)/(x-1)=0[x-m-2(x-1)]/(x-1)=0

2-x-m)/(x-1)=0

There is no solution to the equation. x-1=0, then x=1

Substitute x=1 with: 2-1-m=0

m=1

The original vertex of the parabola is called (0,1), and after rotating point b (1,0) 180 degrees, it is (2, silver call-1), which is also the vertex of the new parabola, so the new parabola equation can be set to y=a(x-2) -1, and the new parabola is also b(1,0), and the substitution is 0=a(1-2) -1, and the solution is a=1

So the equation for the new parabola is y=(x-2) -1=x -4x+3

According to the known conditions, the analytic formula of the parabola can be y=ax 2--- the coordinates of the intersection of the water surface and the parabola in the fourth quadrant are (2,-2), and substituting -2=4a is obtained

The solution yields a=-1 2

So the analytic formula of the parabola is y=(-1 2)x 2

ae=ab,ad=ac, dac= cab, so ade= abc, so bc=de

So cd=cb, so dbc=y=1 2 dab

Let the known fraction = k

Rule. a+b=10k

b+c=11k

c+a=15k

Solution. a=7k

b=3kc=8k

So. a:b:c=7:3:8