Question

已知函数f(x)=x平方 除以ax+b(a,b为常数),方程f( x)-x+12=0的两根为3,4,求f(x)的解析式

Answer 1

f(x)-x+12=0的两根为3,4,所以f(3)-3+12 = 0且f(4)-4+12 = 0

因此f(3) = -9,f(4) = -8

而f(x)=x²/(ax+b),所以

f(3) = 9 / (3a+b) = -9,3a+b = -1 ...①

f(4) = 16 /(4a+b) = -8,4a+b = -2 ...②

由①②解得

a = -1 ,b = 2.

于是f(x)的解析式为f(x)=x²/(2-x).