Factorization (27 14:6:22) 1. (1) prove that 258-514 can be divisible by 24; (2) It is proved that when n is an integer greater than 2, n5-5n3 + 4N can be divided by 120 2. Given a + B + C = 0, prove A3 + A2C + B2C ABC + B3 = 0 3. The sum of two positive integers is 1000 less than the product, and one of them is a complete square number. Try to find the larger number 4. Factorization: x6-y6-2x3 + 1

1. (1) prove that 258-514 can be divisible by 24; is it 25 ^ 8-5 ^ 14 (^ 8 is 8 power, ^ 14 is 14 Power) 25 ^ 8-5 ^ 14 = (5 & sup2;) ^ 8-5 ^ 14 = 5 ^ 16-5 ^ 14 = 5 ^ 14 × (5 & sup2; - 1) = 5 ^ 14 × 24, so 25 ^ 8-5 ^ 14 can be divisible by 24. (2) prove that when n is an integer greater than 2, n5-5n3 + 4N can be integer 120

Calculation: (x-1 / 6y) (2x + 1 / 3Y) (3x ^ 2 + 1 / 12Y ^ 2)

(x-1/6y)(2x+1/3y)(3x^2+1/12y^2)=（2x²-1/3xy+1/3xy-1/18y²)(3x²+1/12y²)=（2x²-1/18y²)(3x²+1/12y²)=6x⁴-1/6x²y²+1/6x²y²-1/216y⁴=6x&#...

What is (- 16) x 17 / 16 x (- 64 / 1)

(- 16) x 17 / 16 x (- 1 / 64)
=16*17/16*1/64
=17*1/64
=17/64

A is a square matrix of two orders. The value of determinant of a is less than 0. It is proved that a is similar to diagonal matrix

Proof: because the value of determinant of a is less than 0
The determinant of a is equal to the product of all its eigenvalues
So a square matrix of order 2 has two different eigenvalues (one positive and one negative)
So a can be diagonalized

The greater the difference, the higher the relative humidity of the air

Small (the drier the air is)

Integral of SiNx square
How can the answer be x / 2 - (sin2x) / 4 + C

∫(sin x)^2 dx
=∫(1-cos 2x)/2 dx
=∫1/2 dx - 1/2 ∫ cos 2x dx
=∫1/2 dx - 1/4 ∫ cos 2x d 2x
=x/2 - (sin2x) / 4 + C

8.2 + 0.8 * (1.4-1.25) simple calculation

8.2+0.8*(1.4-1.25)
=8.2 + 0.8 × (1 + 0.4-1.25)
=8.2+0.8+0.32-1
=8.32

Given that 5x = 3Y, 4Z = 7Y, find X: Y: Z

x：y：z=(3y/5)：y：(7y/4)=(3/5)：1：(7/4)=12：20：35

What is the quotient of 11 out of 12 minus 1 out of 8 multiplied by 1 out of 19 and divided by 2 out of 3?

(11 / 12-1 / 8) * 1 / 19 divided by 2 / 3 = 1 / 16

The parameter equation of circle x ^ 2 + y ^ 2-2x = 0 is?
that,
·····
x^2+y^2-2x=0
(x-1) ^ 2 + y ^ 2 = 1, with (1,0) as the center, 1 as the radius and passing through the origin
Its standard parameter equation is x = 1 + cos α, y = Sina, 0 ≤ α

Oh, this place, because we know
The standard parameter equation is x = 1 + cos α, y = Sina, 0 ≤ α