2(x+1)(x+2)>(x+3)(x+4)
2(x²+3x+2)＞x²+7x+12
2x²+6x+4＞x²+7x+12
x²-x＞8
(x²-x+1/4)＞8+1/4
(x-1/2)²＞33/4
x-1/2＞√33/2
x-1/2＜-√33/2
所以
x＞(1+√33)/2或x＜(1-√33)/2
解不等式2(x+1)(x+2)>(x+3)(x+4)
2(x+1)(x+2)>(x+3)(x+4)
2(x²+3x+2)＞x²+7x+12
2x²+6x+4＞x²+7x+12
x²-x＞8
(x²-x+1/4)＞8+1/4
(x-1/2)²＞33/4
x-1/2＞√33/2
x-1/2＜-√33/2
所以
x＞(1+√33)/2或x＜(1-√33)/2