高一简单数学题

显示全部楼层 · 2010-9-19 19:45:13

比较下列各题中两式值的大小过程写下哦..
1.x(x-y)与y(x-y)(x不等于Y)
2.(3a+1)(a+1)与2(a+1)平方-3
3.(t+1)(t-5)=(t-2)平方.

千问 · 2010-9-19 19:45:13

1. x(x-y) - y(x-y) = (x-y)(x-y) = (x-y)^2 > 0 (因x不等于y) x(x-y) 〉 y(x-y)2. (3a+1)(a+1) -[2(a+1)^2 -3]
= 3a^2 + 4a + 1 -(2a^2 + 4a +2 -3)
= a^2 + 2 > 0
(3a+1)(a+1) > 2(a+1)^2 -33. (t+1)(t-5) - (t-2)^2
= t^2 -4t -5 -(t^2 -4t +4)
= -9 =0;因为x≠y;所以（x+y)^2>0,即x(x-y)>y(x-y)23a+1)(a+1) -[2(a+1)^2 -3]= 3a^2 + 4a + 1 -(2a^2 + 4a +2 -3)= a^2 + 2 > 0所以([3a+1)(a+1)]>=[2(a+1)平方-3]

千问 · 2010-9-19 19:45:13

1、x(x-y)-y(x-y)=x^2-xy-xy-y^2=(x-y)^2>0，所以x(x-y)>y(x-y) 2、(3a+1)(a+1)-[2(a+1)^2-3]=3a^2+4a+1-2a^2-4a+1=a^2+2>0，所以(3a+1)(a+1)>2(a+1)^2-33、(t+1)(t-5)-(t-2)^2=t^2-4t-5-t