Given a + B = 3, ab = - 12, find the value of the following formula （1）a^2+b^2 （2）a^2-ab+b^2 （3）(a-b)^2

Given a + B = 3, ab = - 12, find the value of the following formula （1）a^2+b^2 （2）a^2-ab+b^2 （3）(a-b)^2

（1）a^2+b^2=(a+b)^2-2ab=3^2-2*(-12)=30（2）a^2-ab+b^2 =a^2+2ab+b^2-3ab=(a+b)^2-3ab=3^2-3*(-12)=45（3）(a-b)^2=a^2-2ab+b^2=a^2+2ab+b^2-4ab=(a+b)^2-4ab=3^2-4*(-12)=57

The differentiable function f (x) defined on (0 to positive infinity) satisfies the derivative of x times f (x)

The derivative of x times f (x)

What are the least common multiples of 18 and 15? What are the least common multiples of 17 and 15?

Using short division, divide 18 and 15 by 3 to get 6 and 5 respectively, and the greatest common divisor is 1
3 18 15
6 5
The least common multiple is 3 times 6 times 5, which is 90
Similarly, 17 and 15 are multiplied directly, and the least common multiple is 255

-The reciprocal of 0.17, the reciprocal of 4 and 1 / 4, and the reciprocal of negative 5 and 2 / 5

-The reciprocal of 0.17-100 out of 17
The reciprocal of four and one in four is four in 17
The reciprocal of - 5 and 2 / 5 is - 5 / 27

How to reduce the square of X-Y?
What do you mean by x2?

The square of X - 2XY - the square of Y

How about seven out of eleven times five out of nine plus five out of eleven times two out of nine
It's due on Monday! There's no point

Original formula = 5 / 11 × 7 / 9 + 5 / 11 × 2 / 9
=5/11×(7/9+2/9)
=5/11×1
=5/11

It is known that a and B are integers and A2 + B2 can be divisible by 3

If a and B are not all divisible by 3, then there are two cases: (1) if one of a and B is divisible by 3, let a = 3M, B = 3N ± 1 (m, n are all integers), then A2 + B2 = 9m2 + 9n2 ± 6N + 1 = 3 (3M2 + 3N2 ± 2n) + 1, which is not a multiple of 3, is contradictory; (2) neither a nor B can be divisible by 3. Let a = 3M ± 1, B = 3N ± 1 Then A2 + B2 = (3m ± 1) 2 + (3N ± 1) 2, = 9m2 ± 6m + 1 + 9n2 ± 6N + 1 = 3 (3M2 + 3N2 ± 2m ± 2n) + 2, can not be divisible by 3, which is contradictory; similarly, let a = 3M ± 2, B = 3N ± 1, or a = 3M, B = 3N ± 2, or a = 3M ± 2, B = 3N ± 2, substitute A2 + B2 to get the same conclusion. Therefore, a and B are all multiples of 3

Find the monotone interval of the following five functions: (1) y = 2x + 1 (2) y = 3x ^ 2 + 1 (3) y = 2 / X (4) y
Find the monotone interval of the following five functions: (1) y = 2x + 1 (2) y = 3x ^ 2 + 1 (3) y = 2 / X (4) y = | x-3 | (5) y = 2x ^ 2 + X + 1

(1) From the image is very intuitive, we can see that R monotonically increases
(2) The derivative of Y is 6x; therefore, when x > 0, y = x-3 when x 3; when x 3, y = x-3; when x 0, x > - 0.25, y = x-3; when x 3, y = x-3; when x 3, x 0, x > - 0.25, y = x-3

7.8. Math problems of grade five in primary school
7. 100kg soybean can fry 15kg soybean oil,
(1) How many tons of soybean oil can 10 tons of soybean be fried?
(2) How many tons of soybean oil do you need to fry 10.5 tons of soybean oil?
8. A typist can type a manuscript with 160 words per minute, which can be finished in 25 minutes. If 40 more words per minute, how many minutes can it be finished?
Please list all the above questions

7 (1) 1.5 tons
(2) 70 tons
8 20 minutes

If the sequence a1 + √ 2, a (n + 1) = √ (2 + an) and Liman exists, then Liman is equal to_____ n→∝

liman+1=liman
(an)^2=2+an
(an)^2-an-2=0
(an-2)(an+1)=0
an>0
an=2