Known A root number 1 b 2 b root number 1 a 2 1, proof a 2 b 2 1

Proof: From the title, it can be seen that 0<=a<=1,0<=b<=1;

You might as well set a=sinx, b=siny (x, y are both acute angles), then there is: root number (1-b 2 ) = cosy, root number (1-a 2) = cosx;

So sinx*cosy+siny*cosx=1, i.e., sin(x+y)=1

So x+y=90 degrees.

So a 2 + b 2 = sinx 2 + siny 2 = 1

Ream, 0, 2

a=sinα，b=sinβ

Then the original formula = sin cos + sin cos =1 then sin( +=1, mutual congruence.

i.e. sin = cos

sinβ）^2+（cosβ）^2=1

a^2+b^2=1

By the root number (1-b2

and the root number (1-a 2), the absolute values of a and b are less than 1;

Let a=cos ; b=cosη;

Then: a root number (1-b 2

B root number (1-A 2).

cosθ·sinη

sinθ·cosη

sin(θ+

i.e. sin( +=1;

then + =90°;

then b=cos=cos(90°- =sin;

Rule. a^2+b^2=

sin^2cos^2

a+b=1

a + root number 2b = 2

The two formulas are subtracted and balanced:

Root number 2b-b = 1

b (Gen Wu do number 2-1) talk and laugh = 1

b = root number 2 + 1

a=- root number 2

From the formula (x+y) 2 2(x 2+y 2), we get.

x+y Songbizi(2(x 2+y 2)) 1 2) here, x=(a+1 2) (1 2), y=(b+1 2) (1 2), i.e.

a+1/2)^(1/2)+(b+1/2)^(1/2)≤(2(a+1/2+b+1/2))^1/2)

2a+1+2b+1)^(1/2)

2(a+b)+2)^(1/2)

So, (a+1 2) (1 2)+(b+1 2) (1 Hui slip 2) Ye Jue 2

y= (a+1 sunbend2)+ b+1 2)y 2=a+1 2+b+1 2+2 [(a+1 2)(b+1 2)]1+(a+b)+2 [(a+1 2)(1-a+1 2)]2+2 (3 4+a-a 2).

2+2 [1-(1 liquid pre-2-a) 2].

When then muffled a=1 2, y 2 has a maximum value of 4, i.e., y=2

Because the root sedan number is a + 1 + the root number is b-1 = 0 (according to the range of Dingzhi Xian Lingyi).

So a+1=b-1=0

So a=-1, b=1

Equal a = root number 2 + 1

b=1 (root number 2-1).

b up and down multiplied by the root number 2 + 1 = root number 2 + 1

So equal.

Equality relationship can be rationalized for the b denominator.

Wrong question 1

A is the root number 3B is 1, you say what is the relationship between this and what is not the relationship, but it is wrong.

b=1/(1-√2)=(√2-1)(√2+1)/(1-√2)=-√2-1;

Therefore, if it is the opposite of a, b is chosen

b=1/(1-√2)=(√2-1)(√2+1)/(1-√2)=-√2-1=-a

Therefore, if it is the opposite of a, choose b

Certificate: (A+1)+ B+2) 5

(a+1)+√b+2)]²25

a+1+b+2+2 [(a+1)(b+2)] 25 is obtained from the mean inequality: 2 [(a+1)(b+2)] a+1)+(b+2)2(a+1+b+2) 25

a+b+3≥25/2

a+b 19 2, the inequality holds.

a*2-1 0 and 1-a*2 0 and a+1≠0 So, a*2-1=0 and a+1≠0

a= 1 and a≠-1

So, a=1

substitution, b=0

Then, a+b=1+0=1