A 10 meter long ladder leans against the wall. The vertical distance between the top of the ladder and the ground is 8 meters. After the top of the ladder slides 2 meters, will the bottom slide 2 meters horizontally? Try to explain the reason

A 10 meter long ladder leans against the wall. The vertical distance between the top of the ladder and the ground is 8 meters. After the top of the ladder slides 2 meters, will the bottom slide 2 meters horizontally? Try to explain the reason

According to the meaning of the title, ab = 10m, AC = 8m, ad = 2m, in RT △ ABC, BC = AB2 − ac2 = 102 − 82 = 6 from Pythagorean theorem; when B reaches e, de = AB = 10m, CD = ac-ad = 8-2 = 6m; in RT △ CDE, CE = de2 − CD2 = 102 − 62 = 8, be = ce-bc = 8-6 = 2m

A 10 meter long ladder AB leans against the wall. The vertical distance between the top of the ladder and the ground is 8 meters. How many meters does the ladder slide? The top slide distance = the bottom slide distance

According to the title, the distance from the bottom of the ladder to the wall = square root (10 ^ 2-8 ^ 2) = 6
Let top sliding distance = bottom sliding distance = X
(8-X)^2+(6+X)^2=10^2
It is reduced to x ^ 2-2 * x = 0
X=2

The bottom of the ladder is 25m away from the wall and 7m away. The top sliding distance is equal to the bottom sliding distance. How high is the top from the ground

I think what you are talking about is that the area formed by the ladder and the wall will not change when the sliding distance is equal. Then how high is the top of the ladder from the ground? Let's set the sliding distance from the top to the ground as X. the sliding distance is y.1:25 square = (x + y) square + 492:25 square = x square + (7 + y) square, and then the adjustment is: 1:24 = x + y = > 3: x =

X ^ 2 + ax BX = 0 is decomposed by factorization

x(x+a-b)=0
Then x = 0 or x = b-a
That's it

4X ^ 2-8x-1 and ax ^ 2-bx ^ 2-x factorization

4x²-8x-1
=(2x)²-8x+2²-5
=(2x-2)²-(√5)²
=(2x-2+√5)(2x-2-√5)
ax^2-bx^2-x
=x(ax-bx-1)

Can the original polynomial decompose a factor? 2A + 2B ax + BX = (2a + 2b) - (AX + BX)=

The so-called factorization is to extract the common factors (also called common factors) in several formulas. For example, 2A + 2B = 2 (a + b) and so on

Let a = x-xy, B = XY + Y & #, find: (1) a + B (2) 3a-b

A+B
=x-xy+xy+y²
=x+y²
3A-B
=3x-3xy-xy-y²
=3x-4xy-y²

（x-y）(x²+xy+y²)；（x+y-1）²；（a+1/2）²

（x-y）(x²+xy+y²)=x^3-y^3
（x+y-1）²
=(x+y)^2-2(x+y)+1
=x^2+2xy+y^2-2x-2y+1
（a+1/2）²
=a^2+a+1/4

1. (X & # 178; - XY) △ 2x; 2. (& # 188; a & # 178; B-1 / 3 × AB & # 178;) △ 1 / 12ab = 3a-4b; turn down 3 ↓
3. Polynomial 9x & # 178; + 1 plus a monomial can make it the complete square of an integer, then the added monomial can be______ ?
Supplement: the second question has the process of explaining the answers, and the third one can fill in the blanks directly,

(1) (X & # 178; - XY) △ 2x = (1 / 2) x - (1 / 2) y (2) (&# 188; a & # 178; B-1 / 3 × AB & # 178;) △ 1 / 12ab = (1 / 4 × 12) a ^ (2-1) B ^ (1-1) - (1 / 3 × 12) a ^ (1-1) B ^ (2-1) = 3a-4b (3) 9x & # 178; + 1 want to be a complete square, compare a & # 178; ± 2Ab + B & # 178; ± 6x

Decomposition factor ax & # 178; + ay & # 178; + 2axy-16

ax²+ay²+2axy-16
=a(x+y)²-16
Can't be divided. Is there an a behind 16?
If you don't understand, I wish you a happy study!