For any real number a b find a a b b ab

It can be proved separately to discuss that when a and b are not both 0, a*a+b*b>=2ab and then scaled to a*a+b*b>ab

Then discuss that when both a and b are 0, 0*0+0*0=0*0

So a*a+b*b>=ab, and the equal sign is true if and only if both a and b are 0.

a*a+b*b-2ab=(a+b) squared perfect square formula a+b) squared >= 0

Hence a*a+b*b-2ab >= 0

a*a+b*b>=2ab

2ab>=ab~

So a*a+b*b>=ab

a*a is a positive number and b*b is also positive (all numbers are positive to the 2nd power).

Only when a,b is 0, the two equations are equal.

When a,b are non-zero numbers, a*a+b*b>=ab

First of all, (a-b)*(a-b)>=0, there is a*a+b*b>=2ab;

1) If ab>=0, there is a*a+b*b>=2ab>=ab, it is established;

2) If ab<0, there is a*a+b*b>=0>ab, it is true;

To sum up, a*a+b*b>=ab, the certificate is completed.

Proof: Because the burning wheel is an arbitrary real number a, b has |(a-b)+b|= The front segment is preceded by |a|= So |a|-|b|<=a-b|

1) According to the meaning of the question, it is obtained: Youjing kernel 2 3-x=-2011, and the solution is obtained: x=2017;

2) According to the inscription of the manuscript letter, get: 2x-3<5, solution: x<4

（a-b）²+b-c）²+a-c）²≥0

2（a²+b²+c²）≥2ab+2bc+2ca

a +b +c ab + bc + ca, the equal sign is true if and only if a=b=c.

(a+b) 0, so a + b 2ab, the same way b + c 2bc, a + c 2caThe three inequalities are added and both sides are divided by 2

Exclusion. a, e.g. 1>-2, but the square of 1 is less than the square of (-2).

c, such as 1 2>0, but lg(1 2-0) = lg(1 2), the small roll is absolutely zero.

d, if a, b

With the same sign, 1 A is less than 1 B.

Only b is correct, because (1 2) is a positive number, then the original inequality square lead is invariably unstable.

A error.

Raise. Counterexample. Can. a=1b=-1

Xian Xun made a mistake. b error.

Just give a counter-example.

a=-1b=-2

b/a=2＞1

c Wrong acres are pure mistakes.

Just give a counter-example.

a=2b=1

lg(2-1)=lg1=0d pair.

y=(1/2)^x

This function is:

Subtract the function. Again, a b

So (1 bent celery2) a

1/2)^b

ab does not have to be greater than 0

Therefore, the invocation of teasing in a does not multiply AB by AB on both sides of the equation, and it does not guarantee that it will not be reversed.

Similarly. A does not have to be greater than 0

So b wrong. a>b

i.e. a-b>0

And talk about posture when a-b<1.

C false. So d right.

The reason function y=(1 2) x is a subtraction function.

Difference comparison method.

2a²+2b²+2-2a-2b-2ab

a -2a+1+a -2ab+b +b collapsing oak -2b+1(a-1) +a-b) +b-1).

a-1)²>0

a-b) ²0

b-1)²>0

2a²+2b²+2-2a-2b-2ab>=02a²+2b²+2>=2a+2b+2ab

That is, a + b orange pomace + 1 > = a + b + ab

If and only if (a-1) round shirt quietly = 0

a-b) ²0

b-1) = 0.

i.e. a=b=1

a years old infiltrate b) + (b a).

A 3 + B 3) Calendar Sparrow Grip AB

a+b)(a^2+b^2-ab)/ab

Because (a-b) 2 0

So a 2-2ab + b 2 0

i.e. a2+b2-ab ab

Because it is a positive real number.

So (a2+b2-ab) ab 1

Therefore, (a+b)(a 2+b 2-ab) ab a+b, so (a limb b) +(b a) a+b

Hello! Answer: [D].

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