The operation of integers in grade one 1. The polynomial (|a | - 3) x ^ 3 - (A-3) x ^ 2 + X + 4 is a quadratic trinomial about X. find the value of a ^ 2-2a-3 2. Given that the polynomial MX ^ 3 + 3nxy ^ 2 + 2x ^ 3-xy ^ 2 + y does not contain cubic term, find the value of 2m + 3N

The operation of integers in grade one 1. The polynomial (|a | - 3) x ^ 3 - (A-3) x ^ 2 + X + 4 is a quadratic trinomial about X. find the value of a ^ 2-2a-3 2. Given that the polynomial MX ^ 3 + 3nxy ^ 2 + 2x ^ 3-xy ^ 2 + y does not contain cubic term, find the value of 2m + 3N

1. Because it is quadratic, so | a | - 3 = 0, so a = 3 or - 3,
But this polynomial is quadratic, so A-3 must not be zero,
So a is not equal to 3, only a = - 3 is consistent
=>a^2-2a-3 = (-3)^2-2(-3)-3
= 9+6-3 = 12
2. Since there is no cubic term, both x ^ 3 and XY ^ 2 belong to cubic terms,
So their coefficients should all be 0,
Then M + 2 = 0, = > m = - 2
3n-1=0,=> n=1/3
So, 2m + 3N = - 4 + 1 = - 3

How much is x ^ 2-5x + 2 equal to when x ^ 2 = x + 1 is known in an integral operation problem

We know that x ^ 2 = x + 1
Then x ^ 2-x = 1
x^2-x+1/4=1+1/4
(x-1/2)^2=5/4
x-1/2=±√5/2
x=1/2±√5/2
x^2-5x+2
=x+1-5x+2
=-4x+3
=-4(1/2±√5/2)+3
=-2±2√5+3
=1±2√5

Integral operation: known x square - y square = 6, x + y = 3, then X-Y = say the reason!

x^2-y^2=6
The formula of square difference is as follows:
x^2-y^2=(x+y)(x-y)
Namely
(x+y)(x-y)=6
Substituting x + y = 3
That is, 3 (X-Y) = 6
x-y=6/3=2

If x + 1 x = 3, then the value of x 2 + 1 x 2

x+1x=3       (x+1x)2=32x2+2×x×1x+1x2=9        x2+1x2=9-2        x2+1x2=7．