Prep 2 里面有道DS 数学题不理解

coffee0921

求问　x^4 + y^4 > z^4 ?  (x的4次方＋y 的4次方大于z的4次方否？)下面是两个条件


1. x^2+y^2> z^2
2. x+y > z

newolder

Condition 1: If x = 1, y = 1, z =0; sufficient to prove x^4 + y^4 > z^4.  If x = 4, y = 4, z = 5; insufficient to prove x^4 + y^4 > z^4.  Therefore condition 1 is insufficient.

Condition 2: If x = 1, y = 1, z = 0; sufficient to prove x^4 + y^4 > z^4.  If x = 1, y = 1, z = -3; insufficient to prove x^4 + y^4 > z^4.  Therefore condition 2 is in sufficient.

Combining 1 and 2: If x = 1, y = 1, z = 0; sufficient to prove x^4 + y^4 > z^4. If x = 4, y = 4, z = -5; insufficient to prove x^4 + y^4 > z^4.  Therefore conditions 1 and 2 are not sufficient.