已知 xx2+1 = 12 ,求 x2x4+1 的值.
解:由 xx2+1 = 12 知x≠0,所以 x2+1x =2,即x+ 1x =2.
∴ x4+1x2 =x2+ 1x2 =(x+ 1x )2﹣2=22﹣2=2,故 x2x4+1 的值为 12
评注:该题的解法叫做“倒数法”,请你利用“倒数法”解下面的题目:
已知 xx2−x+1 = 17 ,求 x2x4+x2+1 的值.
阅读下文,回答相关问题。 唐雎不辱使命 《战国策》 ①秦王使人谓安陵君曰:“寡人欲以五百里之地易安陵,安陵君其许寡人!”安陵君曰:“大王加惠,以大易小,甚善;虽然,受地于先王,愿终守之,弗敢易!”秦王不悦。安陵君因使唐雎使于秦。 ②秦王谓唐雎曰:“寡人以五百里之地易安陵,安陵君不听寡人,何也?且秦灭韩亡魏,而君以五十里之地存者,以君为长者,故不错意也。今吾以十倍之地,请广于君,而君逆寡人者,轻寡人与?”唐雎对曰:“否,非若是也。安陵君受地于先王而守之,虽千里不敢易也,岂直五百里哉?” ③秦王怫然怒,谓唐雎曰:“公亦尝闻天子之怒乎?”唐雎对曰:“臣未尝闻也。”秦王曰:“天子之怒,伏尸百万,流血千里。”唐雎曰:“大王尝闻布衣之怒乎?”秦王曰:“布衣之怒,亦免冠徒跣,以头抢地耳。”唐雎曰:“此庸夫之怒也,非士之怒也。夫专诸之刺王僚也,彗星袭月;聂政之刺韩傀也,白虹贯日;要离之刺庆忌也,仓鹰击于殿上。此三子者,皆布衣之士也,怀怒未发,休祲降于天,与臣而将四矣。若士必怒,伏尸二人,流血五步,天下缟素,今日是也。”挺剑而起。 ④秦王色挠,长跪而谢之曰:“先生坐!何至于此!寡人谕矣:夫韩、魏灭亡,而安陵以五十里之地存者,徒以有先生也。”
阅读理解 A Trip to the Forest One day Bob took two of his friends into the mountains. They put up their tents and then rode off to a forest to see how the trees were growing. In the afternoon when they were about ten kilometres from their camp(营地), it started to snow. More and more snow fell. Soon Bob could hardly see his hands before his face. He could not find the road. Bob knew there were two roads. One road went to the camp, and the other went to his house. But all was white snow. Everything was the same. How could he take his friends back to the camp? Bob had an idea. The horses! Let the horses take them back! But what would happen if the horses took the road to his house? That would be a trip of thirty-five kilometres in such cold weather! It was getting late. They rode on and on. At last the horses stopped. Where were they? None of them could tell. John looked around. What was that under the tree? It was one of their tents!