1.若x^2+mx-15=(x+3)(x+n),m的值为几?2．已知x^2+y^2-6x-10y+34=0,则x+y的值是几?3．已知x-1/x=5,求x^2+1/x^2,x^4+1/x^4的值.

Question

1.若x^2+mx-15=(x+3)(x+n),m的值为几?
2．已知x^2+y^2-6x-10y+34=0,则x+y的值是几?
3．已知x-1/x=5,求x^2+1/x^2,x^4+1/x^4的值.

Answer 1

1.若x²+mx-15=(x+3)(x+n),m的值为几?
展开等式右端,得：
x²+mx-15=x²+(n+3)x+3n
左右对比,得：
n+3=m
3n=-15
解之得：
m=-2
n=-5
所以m的值为-2.
2.已知x²+y²-6x-10y+34=0,则x+y的值是几?
x²+y²-6x-10y+34=0
(x²-6x+9)+(y²-10y+25)=0
(x-3)²+(y-5)²=0
由于平方数都大于或等于0,所以上式成立的条件是：
(x-3)²=0,解得：x=3；
(y-5)²=0,解得：y=5；
所以
x+y=3+5=8.
3.已知x-1/x=5,求x^2+1/x^2,x^4+1/x^4的值.
x²+1/x²
=(x-1/x)²+2
=5²+2
=25+2
=27
x^4+1/x^4
=(x²+1/x²)²-2
=27²-2
=729-2
=727