6 (- a square + AB) - 2 (4ab-3a cubic-1)

6 (- a square + AB) - 2 (4ab-3a cubic-1)

6(-a²+ab)-2(4ab-3a³-1)
=-6a²+6ab-8ab+6a³+2
=6a³-6a²-2ab+2

A. B and C are the three sides of triangle. It is proved that the cube of 3A + 6 times the square of a, B-3 times the square of a, c-6abc = 0

3a^3+6a^2b-3a^2c-6abc
=3a(a^2+2ab-ac-2bc)
=3a[a(a+2b-c(a+2b)
=3a(a+2b)(a-c)
If the triangle is isosceles triangle, then the equation holds, if it is a general triangle, then the equation does not hold

Square of a minus 4 divided by square of a plus 4A plus 4

=(a+2)(a-2)/(a+2)²
=(a-2)/(a+2)

Mathematical Olympiad of primary school: remainder formula

There is a formula: the remainder is the same, the sum is the same, the difference is the same, and the common multiple is the cycle
The remainder is the same as the remainder. For example, "a number divided by 7-1, divided by 6-1, divided by 5-1", it can be seen that if the remainder is 1, then 1 is taken, and the expression of the divisor is 210n + 1;
For example, "a number divided by 7 is more than 1, divided by 6 is more than 2, divided by 5 is more than 3". It can be seen that the sum of divisor and remainder is the same. Take this sum 8, and the expression of divisor is 210n + 8;
The difference is the same as subtraction. For example, "a number divided by 7 is more than 3, divided by 6 is more than 2, divided by 5 is more than 1". It can be seen that the difference between divisor and remainder is the same. Take this difference 4, and the expression of divisor is 210n-4;
In particular, 210 is the least common multiple of 5, 6 and 7, which is the period of common multiple!

Sequence {an} general term formula an = (n + 1) 0.9n
The general term formula of sequence {an} is an = (n + 1) × 0.9 * n. is there such a positive integer n
Let an ≤ an hold for any positive integer n? Prove the conclusion

Obviously, this kind of problem is to ask you which item is the largest in the sequence
Let f (n) = (n + 1) 0.9 ^ n, then f '(n) = 0.9 ^ n + ln0.9 (n + 1) 0.9 ^ n
∵ n > 0, ∵ f '(n) > 0. ∵ f (n) increases monotonically on N +
Therefore, there is no qualified integer n
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What's seven eighths plus two fifths

Reference answer:
7/8 + 2/5
=35/40 + 16/40
=51/40

1 minus (A-1 of a) divided by (a + a of 2) - (a square + 1 of 2a)

1 minus (A-1 of a) divided by (a + a of 2) - (a square + 1 of 2a)
=1-(a-1)/a÷[a/(a+2)-1/(a²+2a)]
=1-(a-1)/a÷(a²-1)/a(a+2)
=1-(a+2)/(a+1)
=(a+1-a-2)/(a+1)
=-1/(a+1)

How do 1 to 9 add up to 99

1+2+3+4+5+67+8+9=99

4X + 3Y = 141. If the values of X and Y in the solution of the equation {are equal, find the value of K. KX + (k-1) y = 6
3x-y=7 x+by=a
2. If the equations {and {have the same solution, find the value of a and B
ax+y=b 2x+y=8
Hurry, hurry!

1. The values of X and y are the same, 4x + 3x = 14x = y = 2 ∧ x = y = 2 are substituted into: KX + (k-1) y = 62k + 2 (k-1) = 64K = 8K = 22, 3x-y = 7 （1）2x+y=8…… (2) (1) + (2) we get 5x = 15x = 3Y = 2  3 + 2B = a （3）3a+2=b …… (4) (3) substitute (4) 3 (3 + 2b) + 2 = B9 + 6B + 2 = BB = - 11

Simple calculation of 17 × 19 + 17

17×19+17
=17×(19+1)
=17×20
=340