求y=(x-1)(x-2)(x-3)(x-4)+15的值域

2025-01-19 14:09:30
推荐回答(1个)
回答1:

y=[(x-1)(x-4)][(x-3)(x-2)]+15 =(x^2-5x+4)(x^2-5x+6)+15 =[(x^2-5x+5)-1][(x^2-5x+5)+1]+15 =[x^2-5x+5]^2-1+15 x^2-5x+5=(x-5/2)^2-5/4>=-5/4; 所以[x^2-5x+5]^2>=0; y>=14;