The ladder AB is against the wall. The distance from the bottom a of the ladder to the wall root o is 2m, and the distance from the top B of the ladder to the ground is 7m. Now move the bottom a outward to a ', so that the distance from the bottom a' to the wall root O is 3M, and the top B drops to B ', so BB' is equal to 1m?

AB=√（AO²+BO²）
AB=√53
A′O=3 B′O=√(AB²-A′O²)
B′O=2√11
BB’=7-2√11

As shown in the figure, a 2.5m long ladder leans against the vertical wall. At this time, the bottom of the ladder is 0.7m away from the wall. In order to install the wall lamp, the top of the ladder is 2m away from the ground. Please calculate how far the bottom of the ladder should be pulled away from the wall?

In RT △ DCE, ∵ de = AB = 2.5m, CD = 2m, ∵ CE = de2 − CD2 = 2.52 − 22 = 1.5m. ∵ be = ce-bc = 1.5-0.7 = 0.8m

As shown in the figure, a 2.5m long ladder leans against the vertical wall. At this time, the bottom of the ladder is 0.7m away from the wall. In order to install the wall lamp, the top of the ladder is 2m away from the ground. Please calculate how far the bottom of the ladder should be pulled away from the wall?

In RT △ DCE, ∵ de = AB = 2.5m, CD = 2m, ∵ CE = de2 − CD2 = 2.52 − 22 = 1.5m. ∵ be = ce-bc = 1.5-0.7 = 0.8m

Help to see which formula is used for Factorization x ^ 3 + X-2 = (x-1) (x ^ 2 + X + 2), and which formula is used for 2x ^ 3-3ax ^ 2 + A ^ 3 = (2x + a) (x-a) ^ 2
Help to see which formula is used for Factorization x ^ 3 + X-2 = (x-1) (x ^ 2 + X + 2), and which formula is used for 2x ^ 3-3ax ^ 2 + A ^ 3 = (2x + a) (x-a) ^ 2

X ^ 3 + X-2 = x ^ 3-1 + X-1 = (x-1) (x ^ 2 + X + 1) + (x + 1) = (x-1) (x ^ 2 + X + 2) the first one uses factorization, cubic difference formula and factorization 2x ^ 3-3ax ^ 2 + A ^ 3 = 2X ^ 3-2ax ^ 2-ax ^ 2 + A ^ 3 = 2x ^ 2 (x-a) - A (x ^ 2-A ^ 2) = 2x ^ 2 (x-a) - A (x-a) (x + a) = (x-a) (2x ^ 2-ax-a ^ 2) = (x-a)

Given that 2x ^ 2 + 3xy-2y ^ 2 + ax + by + 12 can be factorized, all the possible values of (a, b) can be obtained

There are 12 possibilities
∵12=1*12
=12*1
=（-1）*（-12）
=（-12）*（-1）
=3*4
=4*3
=（-3）*（-4）
=（-4）*（-3）
=2*6
=6*2
=（-2）*（-6）
=（-6）*（-2）
There are 12 possible values of (a, b)

Given that x = 2 is, the value of the algebraic formula - ax & sup3; - [7 - (BX + 2aX & sup3;)] is 5, find the value of the algebraic formula when x = - 2

-ax³-【7-（bx+2ax³）】
=-ax³-【7-bx-2ax³】
=-ax³-7+bx+2ax³
=ax³+bx-7
When x = 2, the value of the algebraic formula - ax & # 179; - [7 - (BX + 2aX & # 179;)] is 5,
a(2)³+b(2)-7=5
8a+2b=12;
When x = - 2,
-ax³-【7-（bx+2ax³）】
=ax³+bx-7
=a(-2)³+b(-2)-7
=-8a-2b-7
=-(8a+2b)-7
=-(12)-7
=-19.

It is known that when x = 2, the value of the algebraic formula - ax ^ 3 - [7 - (BX + 2aX ^ 3)] is 5, then when x = - 2, the value of the algebraic formula is obtained

The original formula = - ax & # 179; - 7 + BX + 2aX & # 179;
=ax³+bx-7
∵ when x = 2, the value of the algebraic formula - ax ^ 3 - [7 - (BX + 2aX ^ 3)] is 5
∴8a+2b-7=5
8a+2b=12
When x = - 2, the original formula = - 8a-2b-7 = - 12-7 = - 19

In the algebraic expression ax + B, when x = 2, its value is 3; when x = 3, its value is 7, then when x = 1 / 2, what is the value of AX + B?
Do it with a quadratic equation of two variables

2a+b=3.(1)
3a+b=7.(2)
(2)-(1)：a=4
Substituting (1): 2 * 4 + B = 3
b=-5
When x = 1 / 2
ax+b
=4×1/2-5
=-3

Factorization factor ax ^ 2-ax + BX ^ 2 + cxy CX ^ 2-bxy

Factorization of AX + bxy + BX + ax

ax+bxy+bx+axy =ax(1+y)+bx(y+1)=x(a+b)(1+y)