The exact answer is 39/50, and the choices don't seem to contain this, so we choose 7/9. Anyway I will put what you say in the later version. Thank you!
92 DS:x^2是否rounded to 9?
条件1:x^3round to 27
条件2:x round to 3
树桃菌:
条件2显然不成立,比如x=2.5。然后考虑条件1。直观上看条件1肯定是对的,但也需要严格证明。
记A=x³-27=(x-3)(x²+3x+9),B=x²-9=(x-3)(x+3) ,有A-B=(x-3)(x²+2x+6),实际上对于x²+2x+6这部分来说,因为它等于(x+1)²+5,所以是恒正的。当x<3时,A-B是负数,也就是x³与27之间的差值大于x²与9之间的差值,x>3时也一样。换句话说,如果连x³和27之间的差值都已经小于0.5,(可以round to 27),那么x²与9之间的差值会更小,所以一定能round to 9。选A。