Prove by two or more methods: the absolute value of X + X is greater than or equal to 2 (x is not equal to zero) At the level of a sophomore

Prove by two or more methods: the absolute value of X + X is greater than or equal to 2 (x is not equal to zero) At the level of a sophomore

Method 1: use the sign function (do you know), when the sign function y = x + A / X is greater than 0, the lowest point is (root a, double root a)
Method 2: using derivative, y = x + A / x, when derivative is 1-A / (xsquare), a = 1, 0

It is known that X and Y belong to R. prove x ^ 2 + y ^ 2 > = 2XY with vector

Let x = (a, b) y = (m, n)
Then x & sup2; + Y & sup2; - 2XY = A & sup2; + B & sup2; + M & sup2; + n & sup2; - 2 (am + BN)
=(a-m)²+(b-n)²≥0
Take the equal sign if and only if a = m b = n

Solve equation or inequality,. (x + 3) (X-7) + 8 = (x + 5) (x-1) (X-2) (2x-3) ≥ (2x-5) (x-1) - 1

1. (x + 3) (X-7) + 8 = (x + 5) (x-1) xx-4x-21 + 8 = XX + 4x-5 8x = 5-13 8x = - 8 x = - 1 2, (X-2) (2x-3) ≥ (2x-5) (x-1) - 1 2xx-7x + 6 ≥ 2xx-7x + 5-1 + 6 ≥ + 4 is always true. X is any real number and is the solution of inequality,

Party A and Party B are moving in the same direction. The speed of Party A is 3km / s, and that of Party B is 5km / s. Party A passes through place a at noon, and Party B passes through place a at 2pm. What time in the afternoon can party B catch up with place a? How far is it from place a?

14:00-12:00 = 2 hours
3 × 2 = 6 km
6 (5-3) = 3 hours
14∶00＋3∶00＝17∶00
17:00-12:00 = 5 hours
3 × 5 = 15 km
A: B can catch up with a at 5 p.m., 15 kilometers away from a

Turn 3 / 7 into a decimal. The 2009 digit after the decimal point is ()

Turn 3 / 7 into a decimal. The 2009 digit after the decimal point is (7)
3/7=0.428571428571.
It can be seen that after the decimal point is the infinite circular decimal with 428571 as the cycle
There are 6 numbers, so 2009 = 334 * 6 + 5
So bit 2009 is the fifth bit in the cycle, which is 7

A and B cars leave from ab at the same time. A car travels 90 kilometers per hour, B car travels 60 kilometers per hour. After the first meeting, a car arrives at B two hours later. How many kilometers is the distance between AB and B

Let the first meeting time of two cars be t and the distance between two places be s
90t+60t=S
90t+90*2=S
T = 3 s = 450
So the distance between AB and ab is 450 km

A mathematical problem of Pythagorean law and square root in Grade 8
As shown in the picture, there are two straight poles AB and CD across the river. AB is 20cm high, CD is 30cm high, and the distance between the two poles is 50cm. Now there is an Osprey on each pole. At the same time, they see a small fish floating at e on the river between the two poles. The rain stone flies down at the same speed to capture the fish. As a result, the two Osprey arrive at the same time and catch the small fish. Question: what is the distance between the two poles and E?

If the distance between AB and E is x cm, then the distance between Cd and E is 50-x cm
If the speed is the same and the two Osprey arrive at the same time, the flying distance is equal
So 20 ^ 2 + x ^ 2 = 30 ^ 2 + (50-x) ^ 2
So x = 30cm
The distance between AB and e30cm, CD and e20cm
If you don't look at the picture, there are infinite solutions to this problem
In this case, e, CD and ab must be in the same plane

The two trains run 360 kilometers away from each other at the same time, and meet six hours later. It is known that the speed of train B is 4 / 5 of that of train a, so the speed of train a is less than that of train a
How many kilometers do you travel

The first car runs x kilometers per hour
Speed and time of encounter = distance
6（4/5x+x）=360
9/5x=60
x=60÷9/5
x=100/3

Given that the average of a, B, C, D is 3, and the average of B + 1,2,4, A-1 is 4, then B=

a+b+c+d=12
（b+1）+2+4+（a-1）=16
Then B + a = 10, C + D = 2
B the specific value cannot be calculated

The sum of 25 consecutive even numbers is 2000. What is the largest even number
No,

104