已知x,y,z,w为正整数,且x答:但z = 4时解得w = 4,不满足z < w,故只有z = 3.得到一组满足条件的解(1,2,3,6).1/x+1/y+1/z+1/w = 1.首先有x > 1,即x ≥ 2.若x ≥ 3,则y ≥ 4,z ≥ 5,w ≥ 6,1/x+1/y+1/z+1/w ≤ 1/3+1/4+1/5+1/6 = 19/20 < 1.∴ x = 2,y ≥ 3.∵1...
已知x,y,z,w为正整数,且x<y<z<w,求使1/x+1/y+1/z+1/w是正数的所有有序...答:但z = 4时解得w = 4, 不满足z < w, 故只有z = 3.得到一组满足条件的解(1, 2, 3, 6).1/x+1/y+1/z+1/w = 1.首先有x > 1, 即x ≥ 2.若x ≥ 3, 则y ≥ 4, z ≥ 5, w ≥ 6, 1/x+1/y+1/z+1/w ≤ 1/3+1/4+1/5+1/6 = 19/20 < 1.∴ x = 2...