1. If we decompose X & # 178; - 8x + m into (X-5) (x + n), we can find the value of M and N. 2. We know that M & # 178; + n & # 178; + 6m-10n + 34 = 0 The values of (M + n) ² (m-n) ² - (m-n) (M + n) (M & #178; + n & #178;)

1. If we decompose X & # 178; - 8x + m into (X-5) (x + n), we can find the value of M and N. 2. We know that M & # 178; + n & # 178; + 6m-10n + 34 = 0 The values of (M + n) ² (m-n) ² - (m-n) (M + n) (M & #178; + n & #178;)

1.x^2-8x+m=(x-5)(x+n)
x^2-8x+m=x^2-(5-n)-5n
The contrast coefficient is as follows:
5-n=8
-5n=m
The solution is as follows
n=-3
m=15
2.m²+n²+6m-10n+34=0
(m²+6m+9)+(n²-10n+25)=0
(m+3)^2+(n-5)^2=0
Solution
m+3=0
n-5=0
m=-3
n=5

If we know that the expansion of (X & # 178; + NX + 3) (X & # 178; - 3x + m) does not contain X & # 178; and X & # 179; terms, then M =______ ,n＝______ .
Seeking explanation

（x²＋nx＋3）（x²﹣3x＋m）
=x⁴-3x³+mx²+nx³-3nx²+mnx+3x²-9x+3m
=x⁴+(n-3)x³+(m-3n+3)x²+(mn-9)x+3m
∵ expansion does not contain X & # 178; and X & # 179; terms
∴n-3=0,m-3n+3=0
∴n=3,m=6

If we know that the expansion of (X & # 178; + NX + 3) (x-3x + m) does not contain X & # 178; and X & # 179; terms, then M =, n=

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