Given (A & # 178; + B & # 178;), # 178; - (A & # 178; + B & # 178;) - 6 = 0, then the value of a & # 178; + B & # 178; is

Given (A & # 178; + B & # 178;), # 178; - (A & # 178; + B & # 178;) - 6 = 0, then the value of a & # 178; + B & # 178; is

(A & \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ා178; = 3

Given (A & # 178; + B & # 178;) - (A & # 178; + B & # 178;) - 6 = 0, what is the value of a & # 178; + B & # 178

Solution;
∵(a²+b²)²-(a²+b²)-6=0
1 -3
1 2
Crisscross
∴[(a²+b²)-3][(a²+b²)+2]=0
∵a²+b²+2>0
∴a²+b²=3

Given (A & # 178; + B & # 178;), # 178; - (A & # 178; + B & # 178;) - 6, find the value of a & # 178; + B & # 178;)

When the value of a and B is, a & # 178; + 2B & # 178; - 3A + 6B + 25 has the minimum value, and the minimum value is obtained

a²+2b²-3a+6b+25
=a²-3a+9/4+2b²+6b+9/2+18.25
=(a-3/2)²+2(b+3/2)²+18.25
So when a = 3 / 2, B = - 3 / 2, the minimum value is 18.25

A (a-2b) + 2 (a + b) (a-b) + (a + b) & # 178;, where a = - & # 189;, B = 1
Ask the great God to answer

If a + B = 6, a & # 178; + B & # 178; = 18, then a + B =?

a×b=6
a²+b²=18
∴(a+b)²
=a²+b²+2ab
=18+2×6
=30
∴a+b=√30
Or a + B = - √ 30

（a²+b²）²-（a²+b²）-6=0 a²+b²=?

(A & # 178; + B & # 178;) &# 178; - (A & # 178; + B & # 178;) - 6 = 0, you can take (A & # 178; + B & # 178;) as X, the original problem becomes X & # 178; - X-6 = 0, then you find that this is (x-3) × (x + 2) = 0, and then you know the answer is 3 and - 2, but you look carefully and find that this x is two positive

4.-(a+1)²+9(a-2)²
The question just now has been swallowed by Baidu

-(a+1)²+9(a-2)²
=9(a-2)²-(a+1)²
=[3(a-2)+(a+1)][3(a-2)-(a+1)]
=[3a-6+a+1][3a-6-a-1]
=(4a-5)(2a-7)

If A-B = √ 3, B-C = √ 2, a + C = √ 3 - √ 2, then a & # 178; - B & # 178=

a-b=√3,----(1)
b-c=√2,----(2)
a+c=√3-√2----(3)(
1)+(2)+(3),2a=2√3,a=√3
√3-b=√3,b=0
a²-b²=(√3)²-0=3

Given A-B = 2, B-C = - 3, then 1 / 2 [(a-b) &# 178; + (B-C) &# 178; + (A-C) &# 178;]=
Given that the rational numbers a and B satisfy the absolute value of A-1 × 10 & # 179; + (B + 1) &# 178; × 10 to the fourth power = 0, then the 101st power of a + the 102nd power of B=

a-b=2,b-c=-3
Then a-c = - 1
Original formula = 1 / 2 (4 + 9 + 1) = 7
Second question:
There is A-1 = 0
b+1=0
a=1,b=-1
Then the original formula = 1-1 = 0