Factorization: 800 ^ 2-2x800x799 + 799 ^ 2

Factorization: 800 ^ 2-2x800x799 + 799 ^ 2

800^2--2*800*799+799^2=(800--799)^2
=1^2
=1.

Factorization solution equation (x ^ 2-x) ^ 2 = 4 (2x ^ 2-2x-3) write the detailed process

Let u = x ^ 2-x
u^2=4(2u-3)
u^2-8u+12=0
U = 6 or u = 2
(1)x^2-x-6=0
X = 3 or x = - 2
(2)x^2-x-2=0
X = 2 or x = - 1
To sum up, x = - 1 or - 2 or 2 or 3

Factorization solution equation, 2x ^ 2 + x = 0 (x + 1) ^ 2-2 (x + 1) = 0 x ^ 2-3x + 2 = 0

2x^2+x=0
x(2x+1)=0
x=0,x=-1/2
(x+1)^2-2(x+1)=0
(x+1)(x+1-2)=0
(x+1)(x-1)=0
x=-1,x=1
x^2-3x+2=0
(x-2)(x-1)=0
x=2,x=1

(x-1) (2x + 3) + X (1-x) = 0, factorization solution equation

(x-1)(2x+3)+x(1-x)=0
(x-1)(2x+3)-x(x-1)=0
(x-1)(2x+3-x)=0
(x-1)(x+3)=0
x-1=0 x=1
x+3=0 x=-3

In the triangle ABC, CD and be are respectively the midlines on the sides of AB and AC, extending CD to F, making FD + CD, extending be to g, is be = eg,
Is AF equal to Ag? Are f, a and G in a straight line? Why

Δ DFA is equal to Δ DCB, and Δ EGA is equal to Δ EBC
∴AF=BC ,AG=BC,∴AF=AG
∵ congruent, ∵ fad = ∠ DBC, ∵ EAG = ∠ ECB
∵∠BAC+∠DBC+∠ECB=180°
∴∠BAC+∠FAD+∠EAG=180°
F, a and G are on the same line

Known: a = 10000, B = 9999, find the value of A2 + b2-2ab-6a + 6B + 9

∵ a = 10000, B = 9999, ∵ A-B = 10000-9999 = 1, then the original formula = (a-b) 2-6 (a-b) + 9 = 1-6 + 9 = 4

An elliptic equation passing through point P (2, - 3) and having a common focus with ellipse xsquare / 4 + ysquare / 9 = 1_____________

The focus of ellipse x square / 4 + y square / 9 = 1 is (0, soil √ 5),
Let x ^ 2 / b ^ 2 + y ^ 2 / (b ^ 2 + 5) = 1,
It passes through P (2, - 3),
∴4/b^2+9/(b^2+5)=1,
It is reduced to (b ^ 2 + 2) (b ^ 2-10) = 0,
The solution is B ^ 2 = 10
The elliptic equation is x ^ 2 / 10 + y ^ 2 / 15 = 1

As shown in the figure, in △ ABC, ad ⊥ BC, it is known that ∠ ABC ＞ ACB, P is any point on AD

It is proved that: take DB ′ = dB on DC, connect Pb ′, ab ′ and intersect PC at point e. from the axial symmetry, we can know that Pb ′ = Pb, ab ′ = ab. from the triangle trilateral relation theorem, we get AB + PC = ab ′ + PC = AE + EB ′ + PE + EC > Pb ′ + AC = Pb + AC

Let f (x) = ax ^ 3 + BX ^ 2-3a ^ 2x + 1 (a, B ∈ R) take the maximum value at x = x1, x = X2, and | x1-x2 | = 2, if a > 0, find the value range of B
Let f (x) = ax ^ 3 + BX ^ 2-3a ^ 2x + 1 (a, B ∈ R) take the maximum value at x = x1, x = X2, and | x1-x2 | = 2, if a > 0, find B
Value range of

Analysis: consider the derivative + inequality, f (x) = ax ^ 3 + BX ^ 2-3a ^ 2x + 1, get f '(x) = 3ax ^ 2 + 2bx-3a ^ 2, discriminant = 4B ^ 2 + 36a ^ 3 > 0, and f (x) get the maximum value at x1, X2. Get f' (x) = 0, there are two, and X1 + x2 = - 2b / (3a), x1x2 = - A

If the radius of the inscribed circle of the triangle is R and the lengths of the three sides are a, B and C respectively, then the area of the triangle is s = 12R (a + B + C). According to the analogy, if the radius of the inscribed sphere of the tetrahedron is R and the areas of the four sides are S1, S2, S3 and S4 respectively, then the volume of the tetrahedron is v = 12R___ ．

Let the center of the inscribed sphere of a tetrahedron be o, then the distance from the center O to the four faces is r, so the volume of the tetrahedron is equal to the sum of the volumes of four triangular pyramids with o as the vertex and four faces as the bottom respectively. So the answer is: 13R (S1 + S2 + S3 + S4)