The value of ∣ m + n ∣ can be obtained by knowing (M + N + 5) (M + N + 5) = 144

The value of ∣ m + n ∣ can be obtained by knowing (M + N + 5) (M + N + 5) = 144

（m＋n＋5）(m＋n＋5)=144
That is, (M + N + 5) & sup2; = (± 12) & sup2;
So m + N + 5 = ± 12
m+n=-5±12
That is, M + n = - 5 + 12 = 7 or - 5-12 = - 17
So | m + n | = 7 or 17

There are three kinds of goods: A, B and C. If you buy 3 pieces of a, 7 pieces of B and 1 piece of C, it costs 315 yuan in total. If you buy 4 pieces of a, 10 pieces of B and 1 piece of C, it costs 420 yuan in total. How much is each piece of a, B and C?

3x+7y+z=315…… a
4x+10y+z=420…… b
B-A was obtained
x+3y=105…… c
A-2c was obtained
x+y+z=95

Algebra (23 19:50:52)
A (A-2) - (A & # 178; - 2b) = - 4. Find the algebraic formula & # 189; (A & # 178; + B & # 178;) - ab

From a (A-2) - (A & sup2; - 2b) = - 4
a²-2a-a²+2b=-4
-2a+2b=-4
-2(a-b)=-4
a-b=2
∴(a-b)²=a²+b²-2ab=4
∴½（a²+b²)-ab =(a²+b²-2ab)÷2=2

If the numbers a &# 160; &# 160; B are opposite to each other, and the numbers C &# 160; &# 160; &# 160; D are reciprocal to each other, then what is the third power of (a + b) and the second power of (CD)?
 

If the numbers a and B are opposite to each other, then a + B = 0
If C and D are reciprocal, then CD = 1
therefore
[(a+b)/100]^3-1/(cd)^2
=[0/100]^3-1/(1)^2
=0-1
=-1