When Xiao Fang calculates a + bc-a ^ 2 / A ^ 2 + B ^ 2 + C ^ 2 (a, B, C are not equal to each other), he finds that if a and B are exchanged, the value of this formula remains unchanged, If a + B + C = 1, the constant value a + (bc-a ^ 2 / A ^ 2 + B ^ 2 + C ^ 2) bc-a ^ 2 is a molecule

When Xiao Fang calculates a + bc-a ^ 2 / A ^ 2 + B ^ 2 + C ^ 2 (a, B, C are not equal to each other), he finds that if a and B are exchanged, the value of this formula remains unchanged, If a + B + C = 1, the constant value a + (bc-a ^ 2 / A ^ 2 + B ^ 2 + C ^ 2) bc-a ^ 2 is a molecule




Construct an algebraic expression containing the letters P and Q, so that no matter what the values of P and Q are, the value of the algebraic expression is always negative. How many such algebraic expressions can be written? (if finite, list all, if infinite, explain the reason)


-P & # 178; Q & # 178; - 1. Infinite, as long as P and Q are even power, so that the product of even power of (PQ) must be greater than or equal to 0, plus a negative sign before it must be less than or equal to 0, and minus a positive number after it, it must be less than or equal to 0



This paper constructs an algebraic expression containing the letters P and Q, so that no matter what the values of P and Q are, the value of the algebraic expression is always negative. How many such algebraic expressions can be written?


-lpl-lql
-p^2-q^2
-lpl-q^2
-p^2-lql



Decomposition factor (x + 2Y) &# 178; - X & # 178; - 2XY - 7m (m-n) &# 179; + 21mn (n-m) &# 178; (3a-4b) (7a-8b) + (11a + 2b) (8b-7a)


Thank you



2m-3


M is less than - 9



2m-3=7m-3/2
solve equations:
2m-3=7m-3/2


  2m-3=7m-3/2
2m-7m=-3/2+3
-5m=3/2
m=-3/10



9a-5+4a;
(2) Simplification: 9a-5 + 4a; 3Y * 6 + 4Y
(3) Simplification: the square of 8x - 5x * 2


9a-5+4a
=13a-5
3y*6+4y
=18y+4y
=22y
The square of 8x - 5x * 2
=8x^2-10x
=2x(4x-5)



First simplify and then evaluate: 3 (M + 1) ^ 2 + 4 (M + 1) (m-1) - 7m (m-1), where M = 2
The main is to simplify the process, must be detailed, as for what can be substituted into the evaluation without


3(m+1)^2+4(m+1)(m-1)-7m(m-1)
=3(m^2+2m+1)+4(m^2-1)-7m^2+7m
=3m^2+6m+3+4m^2-4-7m^2+7m
=13m-1
When m = 2
simple form
=13*2-1
=25



It is known that a, B and C are real numbers of incomplete equality, and it is proved that: (B + C-A) / A + (c + a-b) / B + (a + B-C) / C > 3
Come on, I'm going crazy





Given that A.B.C is a real number and √ A & # 178; - 2a-3 +| B + 1 | + (c + 2) &# 178; = 0, find the roots of the equation a χ & # 178; + B χ + C = 0
(A-3) in the radical


√a²-2a-3 +| b+1 |+﹙c+2﹚²=0
So a & # 178; - 2a-3 = 0, B + 1 = 0, C + 2 = 0
So a = - 1 or 3 B = - 1 C = - 2
When a = - 1, a χ & # 178; + B χ + C = 0, that is - X & # 178; - X-2 = 0, the discriminant less than 0 has no solution
When a = 3, a χ & # 178; + B χ + C = 0, that is, 3x & # 178; - X-2 = 0, the solution is x = 1 or x = - 2 / 3
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