Mathematics defines new operations in the first year of junior high school, and defines new operatio

Solution: (1)5*7=5 7-(5+7)=23 7*5=7 5-(7+5)=23 (2)12*(3*4)=12*[3 4-(3+4)]=12*5=12 5-(12+5)=43 (12*3)*4=[12 3-(12+3)]*4=21*4=21 4-(21+4)=59 (3) From the above calculation, there is a commutative law, There is no associative law. (Simplification:.)

3*（5*x）=8x-13=3 x=2

I also kind of can't do it, but to give you some information, I don't know if you can see if you can do it:

Defining a new operation means representing a new operation with a symbol and a known operation expression. For example, let a b=a+b+ab 3 2=3+2+6=11 5 5=5+5+25=35

Example: Defining a new operation can be a class of mathematical problems, such as: x,y represents two numbers, prescribing a new operation"*"and"△"As follows:

x*y=mx+ny, x y=kxy, where m, n, k are all natural numbers, known 1*2=5, (2*3) 4=64, find the value of (1 2)*3. Analysis We use the analysis method, starting from the required question, the question requires the value of (1 2) * 3, first we have to calculate 1 2, according to"△"Definition: 1 2=k 1 2=2k, since the value of k is not known, the value of k must be calculated first.

After the value of k is calculated, the value of 1 2 is calculated, and we let 1 2=a(1 2)*3=a*3, press"*"Definition: a*3=ma+3n, we can only calculate the value of a*3 when we find m,n.

So to calculate the value of (1 2)*3, we need to find the value of k,m,n first. The value of m,n can be found by 1*2 =5, and the value of k can be found by (2*3) 4=64. Solution Because 1*2=m 1+n 2=m+2n, there is m+2n =5

And because m and n are both natural numbers, we solve: When m=1, n=2: (2*3) 4=(1 2+2 3) 4 =8 4=k 8 4=32k has 32k=64, and k=2

When m=3,n=1: (2*3) 4=(3 2+1 3) 4 =9 4=k 9 4=36k So m=l,n=2,k=2. (1△2)*3=(2×1×2)*3 =4*3 =1×4+2×3 =10.

I don't know if the number 1 is defined so that for any number a there is a*1 a, if so, the answer is yes.

3 4 (i.e. 3 to the 4th power), a bit like recent algebra!

1.Not equal. From the previous formula, k is equal to 4, and substituting the latter calculation is 8 5=

2.If you want to subtract 3a+kb=3b+ka, the equation holds when k=3.

23 2343 59 has an exchange rate and no associative law 2

It is to imitate it, which is learned in the Olympiad. For example: a b = 2a + 2b

The greatest common divisor of 18 and 12 is 6, and the least common multiple is 36, so 18 & 12 = 6 + 36 = 42

*7=5x7-（5+7）=23

7*5=7x5-（7+5）=23

（3*4）=12*（3x4-4-3）=12*5=12x5-12-5=43

12*3）*4=（12x3-12-3）*4=21*4=21x4-21-4=59

3. There is a commutative law, reason:

a*b=axb-（a+b），b*a=bxa-（b+a）

So a*b=b*a

There is no associative law, reason:

a*（b*c）=a*(bc-b-c)=a(bc-b-c)-(a+bc-b-c)=abc-ab-ac-a-bc+b+c

a*b)*c=(ab-a-b)*c=(ab-a-b)c-(ab-a-b+c)=abc-ac-bc-c-ab+a+b

So (a*b)*c is not equal to a*(b*c).

4. Let 5*x=y, 3*y=3y-3-y=3

The solution is y=3, i.e., 5*x=5x-5-x=3

Indicates to the left, so 2009? Zhenqi 2008=2009

Indicates to the right, so the grandson is blind to 2007! 2006=2006

In summary, the air (2009?) 2008)?(2007!2006)=2009

The villain to the left is also quick to move? The meaning is to take the number of the left mu beam side, and the villain to the right is also! The meaning is to take the number on the right, the potato is large.

Therefore (2009?) 2008)?(2007!2006)

The question mark indicates the number on the left....Preferential, C-like short-circuit. You don't need to look at the right expansion number, the leftmost number is 2009

Pro, it's not "+", it's "", it's "", it's a solution:

Known: 1 1=1, (n+1) 1=3(n 1), n=1:

When n=2:n=3:

n=4: while: 81= 9

i.e.: (5 1) = 9

Method 2: 1*1=1

As you can see, when n is increased by 1, the result is 3 times the original.

Therefore 5*1=3 3 3 3

It is to imitate it, which is learned in the Olympiad. For example: a b = 2a + 2b 2

That's the title, right?

Solution: Known: 1 1=1, (n+1) 1=3(n 1), n=1:

When n=2:n=3:

n=4: while: 81= 9

i.e.: (5 1) = 9

x+y) (x-y) 3x ruler[3(x y) 2(x y)] clap shout 3x (5x y) 3x 3(5x y) 2 3x 21x 3y

Raid on the Wild Election C

Parsing -2 3=-2x3-2x3

So 4 -12 = 4x-12 - (2x-12) = -48 + 24

Hope it helps.

Learning progress o ( o thank you.

There's something wrong with the title.

If a=c=b=d is specified, a new operation is defined.

then p=1 q=2

Then (1,2) (p,q)=(-3,,4) should define the new operation when a=c b=-d.

then (1,2) (p,q)=(5,0).

p-2q=5

q+2p=0

Then the operation results in p=1 q= -2

It is defined as (1,2) (p,q)=(p-2q,2p+q) and because (1,2) (p,q)=(5,0).

So p-2q=5 ,2p+q=0

So p=1, q=-2

1*p-2*q=5

1*q+2*p=0

Lianli is available. p=1q=-2

Give a good review, o( o thank you.