In the triangle ABC, the opposite sides of the angle a.b.c. are a.b.c. and satisfy that a square plus b square plus a must be equal to C square to find the angle C

In the triangle ABC, the opposite sides of the angle a.b.c. are a.b.c. and satisfy that a square plus b square plus a must be equal to C square to find the angle C


A square plus b square plus a must equal C square
- -------
a^2+b^2+ac=c^2
a^2+b^2-c^2=-ac
cosC=(a^2+b^2-c^2)/2ac
=(-ac)/2ac
=-1/2
C=120°



In the triangle ABC, a = m square - n square, B = m square + n square, when C = what, angle B = 90 degrees
It's a process


c^2=(m^2+n^2)^2-(m^2-n^2)^2 c^2=m^4+n^4+2m^2n^2-(m^4+n^4-2m^2n^2) c^2=2m^2n^2+2m^2n^2 c^2=4m^2n^2 c=2mn



In the triangle ABC, if AB = the square of M - the square of N, AC = 2Mn, then the triangle ABC is a sub triangle, which angle is 90 degrees


This is an uncertain triangle
According to the known conditions: M > n > 0
Let m = 3, n = 1, then: ab = 8, AC = 6, the value range of BC is: 0



Let u = arctan (x + YZ), then &; ^ 3Z / &; X &; Y &; Z=
Let u = arctan (x + YZ), then &; ^ 3Z / &; X &; Y &; Z=


Is it &; ^ 3U / &; X &; Y &; Z=
If it is, first find; ^ u /; X = 1 / (1 + (x + YZ) ^ 2)
And then find the following formula: &; ^ 2U / &; X &; y = - 2Z (x + YZ) / (1 + (x + YZ) ^ 2) ^ 2
And then find out the following formula: z = (8yz (x + YZ) ^ 2-2 (x + 2yz)) / (1 + (x + YZ) ^ 2) ^ 3



(75%x -56)/x=2/(2+3)


(75%x -56)/x=2/(2+3)
2x=5(0.75x-56)
2x=3.75x-280
1.75x=280
x=160



Why is dividing by a number equal to multiplying by the reciprocal of that number?
Yes, please


A number divided by N is equivalent to dividing the number into N parts. A number multiplied by 1 / N is equivalent to dividing the number into N parts and picking out one of them



Solving ordinary differential equation: y '+ 2XY + 2 (x ^ 3) = 0
This is a first order linear differential equation. I do not like the answer, want to seek the process, know how to do!


(constant variation method)
∵y'+2xy=0 ==>dy/y=-2xdx
==>LNY = - 2x & sup2; + LNC (C is an integral constant)
==>y=Ce^(-x²)
Let the general solution of the differential equation y '+ 2XY + 2 (x ^ 3) = 0 be y = C (x) e ^ (- X & sup2;) (C (x) denotes a function of x)
∵y'=C'(x)e^(-x²)-2xC(x)e^(-x²)
Substituting into the original equation, C '(x) e ^ (- X & sup2;) + 2x & sup3; = 0
==>C'(x)=-2x³e^(x²)
==>C(x)=-2∫x³e^(x²)dx
=-∫x²e^(x²)d(x²)
=-X & sup2; e ^ (X & sup2;) + ∫ e ^ (X & sup2;) d (X & sup2;) (Application of partial integration method)
=-X & sup2; e ^ (X & sup2;) + e ^ (X & sup2;) + C (C is an integral constant)
=(1-x²)e^(x²)+C
∴y=C(x)e^(-x²)=[(1-x²)e^(x²)+C]e^(-x²)=1-x²+Ce^(-x²)
So the general solution of the differential equation y '+ 2XY + 2 (x ^ 3) = 0 is y = 1-x & sup2; + CE ^ (- X & sup2;) (C is an integral constant)



It is known that a2-6a + 9 and | B-1 | are opposite numbers, then the value of (AB − BA) / (a + b) is______ .


From the meaning of the title, we know that a2-6a + 9 + | B-1 | = (A-3) 2 + | B-1 | = 0, | A-3 = 0, B-1 = 0, | a = 3, B = 1



Each multiplication formula can write two division formulas______ .


According to the multiplication, we can only write one division formula, 9 / 3 = 3



The trajectory equation of a point equidistant from Z axis and a (1,3, - 1) in space rectangular coordinate system?
How to find the trajectory equation of a point equidistant from Z axis and a (1,3, - 1) in space rectangular coordinate system?
(mainly the distance from the point to the z-axis will not be calculated)


x^2+y^2=(x-1)^2+(y-3)^+(z+1)^2