How much is the cubic power of 6x + the quadratic power of X - the cubic power of 3x - 1 x - the cubic power of 3x + 2 x + the quadratic power of 6x + 11x + 6

How much is the cubic power of 6x + the quadratic power of X - the cubic power of 3x - 1 x - the cubic power of 3x + 2 x + the quadratic power of 6x + 11x + 6

The third power of 6x + the second power of x-3x-1
=6x³+3x²-2x²-3x-1
=3x²(2x+1)-(2x+1)(x+1)
=(2x+1)(3x²-x-1)
The third power of x-3x + 2
=x³-x²+x²-3x+2
=x²(x-1)+(x-1)(x-2)
=(x-1)(x²+x-2)
=(x-1)(x-1)(x+2)
=(x-1)²(x+2)
The third power of X + the second power of 6x + 11x + 6
=x³+6x³+9x+2x+6
=x(x+3)²+2(x+3)
=(x+3)(x²+3x+2)
=(x+1)(x+2)(x+3)

The difference between the two equations of x square + 5x + k = 0 is only 5, so we can find the value of K

Let one root of the equation be a, then the other root is a + 5
According to the relationship between root and coefficient, it is concluded that: 1
a+(a+5)=-5
a(a+5)=k
The solution is as follows
a=-5
k=0
In solution 2, two a and a + 5 are substituted into the original equation respectively
a^2+5a+k=0
(a+5)^2+5(a+5)+K=0
The solution is a = - 5
k=0

On the equation of X, one of the squares of X - 5x + k = O follows zero, then the other is?

On the equation of X, one of the squares of x-5x + k = O follows zero. Then, substitute this root into the original equation to get: k = 0, then the original equation is: x ^ 2-5x = 0, and the solution is: X1 = 0, X2 = 5. Therefore, the other root is 5

It is known that the difference between the square of the quadratic equation x + 5x + k = 0 with respect to X is 3, and the value of K is obtained

x1+x2=-5 x1x2=k
∵|x1-x2|=3
That is, (x1 + x2) & #178; - 4x1x2 = 9
25-4k=9
The solution is k = 4