已知函数f(x)=x²+x-1,α,β是方程f(x）=0的两个根（α＞β）f'(x)是f(x）的导数，设a1=1,an+1=an-f(a
解：令g(x)=(x-a)(x-b)，它是一个开口向上的抛物线，g(x)=0的两根为a,b.设a<b.
f(x)=(x-a)(x-b)+2，是g(x)向上平移了两个单位而得到的抛物线，f(x)=0的两根
为α、β，设α<β.由图可知，(α、β)包含于(a,b)，即有a<α<β<b成立。.
设y=（x-a）（x-b）的大致图象如图所示的抛物线①（黑色），它与x轴的交点坐标的横坐标依次为a、b，∴f（x）=（x-a）（x-b）+是由抛物线①向上平移个单位长度得到的．如图中的抛物线②（红色），它与x轴的交点横坐标分别是α，β，∴由图象得a＜α＜β＜b故选B
(1)解析：f(x)=x^2+x-1=0，α=(-1+√5)/2, β=(-1-√5)/2(2)证明：设a1=1, a(n+1)=an-f(an)÷f"(an)(n=1.2.3...)
a(n+1)=[(an)^2+1]/[2an+1]
设g(x)=(x^2+1)/(2x+1)
令g’(x)=2(x^2+x-1)/(2x+1)^2=0
X1=α>0, x2=β<0
∵g’’(x1)>0,∴函数g(x)在x1处取极小值g(α)=α≈0.618
∴当x>α时，函数g(x)单调增
∴当x=n (n∈N+)时，g(x)> α
即对任意的正整数n都有an＞α成立。
1, throat dry throat when
dumb drink salt water; Service honey Li Gao; drink orange peel Ribes.
2, when the sore throat
eat pears can prevent sore tongue and sore throat; with the same amount of water, vinegar rinse, reduce pain; soft loofah smashed Ji Zhi, frequently rinse; throat pain, gargle can be a spoonful of sauce, about 1 minute rinse spit out 3-4 times a row, is curative.
3, mouth blisters when
slices ginger imported chewing, can gradually eliminate blisters; before going to wash my face, squeeze point at the ointment applied to the lips of pain, pain the next day will be reduced, continue to apply for a few days, make the pain disappear.
4, stuffy nose difficult as following through when
nostril blocked, viable prone position or the right lateral position, the right hand grabbed the back of the neck, heel close to the ear lobe, hold up the head, face right, extended to the right elbow, stretching far as possible. The role of the meridian of the stretch, at least ten seconds, as many as tens of seconds, you can make the nose ventilation. Such as the right side of the nasal congestion, you can rule contrary actions. Both sides of the same stuffy nose, can have rotation movement rule
5, chapped lips
Recommended: cucumber kiwi juice
practices: cucumber 200 grams, 30 grams of kiwi fruit, cold water 200 ml, two tsp of honey. Wash seeded cucumber, leaving skin into small pieces, kiwi fruit peeled and cut, together into the juicer, add cold water mixing, pouring an hour before a meal by adding honey to drink.
cucumber sex Ganliang,Mac foundation, can go into the spleen and stomach by, can heat detoxification, diuresis. Treat fever, thirst, sore throat. The kiwifruit of Gly cold, to get into the kidneys and stomach, fever and thirst quencher function, so the two combined to run the lips. Other vitamin-rich fruits and vegetables can also be used, such as tomatoes, grapefruit and so on.
Reminder: Do not use dry lips, tongue licking, that will only become more dry.
6, dry itchy skin
Recommended: fried sweet potato, melon milk (young cucumber)
practices: sweet potato 300 grams, 100 grams of milk melon, coriander leaves, spring onion , minced garlic. Sweet potatoes, milk melon cut into pieces; oil into a hot place four minced garlic, spring onion, stir-fried pieces of sweet potato into five maturity and then into the milk melon stir well, add the amount of water, salt, chicken, sauce is dry can be.
Comments: sweet potato contains a variety of vitamins and calcium, phosphorus and iron, their sexual gamping non-toxic, can Qiangshen spleen tonic, while the tender cucumber also contains a lot of vitamins, so the skin has a certain benefits.
Reminder: Do not hard scratch itchy skin, broken susceptible to scratching.
7, hair dry
Recommended: candied walnut soup
practices: dates 250 grams, 100 grams of walnut, sugar amount. The dates to go nuclear, wash and drain; with walnut, sugar pot with a small stew; be thick soups, walnut foam off the fire eating. This soup nourishing liver and kidney, lungs and fluid,Dior sunglasses, nourishing conditioner.
of sweet warm walnut can into the kidney by the liver and lungs, can be laxative, but also blood and black hair, Jiufu can make the skin smooth and delicate. The dates can Bufei dryness, so the benefits of more hair. In addition, other nuts, fish and whole grains, there are many benefits to the hair.
8, dry throat, swollen
recommend: honey Li Gao
approach: Take pears, pear juice with the juice squeezed into a suitable amount of honey to slow fire brewed into a paste. A spoonful a day, to clearing away heat, fluid and throat.
Comments: honey Gan Ping, lung and spleen into the large intestine, can relax bowel, throat and lungs, but also detoxification. Pear willing to cool slightly acidic, into the lung and spleen after, can cure cough, thirst, constipation. So the two can play together Aogao role throat. Fresh green leafy vegetables, cucumber, orange, green tea, pears, carrots have a good clear fire role.
reminder:
9, nose bleeding
recommended: fruit sago
practices: Wash sago, pour boiling water; cooked to translucent West, the West rice and water are separated; cook a pot of boiling water, cook to translucent West will pour boiling water until transparent, the boiling water is tossed away; cook a pot of milk and add a little sugar; the West poured into the milk boil boil; the cooked sago milk let cool, add fruit D, you can.
with some cool fruit such as pears, oranges, apples, kiwi fruit, banana hot clear solution, together with sago and milk nourishing the stomach, is a good way to winter conditioning. Eating of cold food, such as radish, lotus seeds, preserved eggs, etc. can be effectively alleviated.
Reminder: Do not drink a lot of cold drinks, to prevent stomach injury.
10, other
tea excitable nerve center, fatigue, heat Reduce Pathogenic Fire, throat thirst, do not sleep thinking ability; tea can add a variety of vitamins, to improve the quality of human health ; tea can promote food intake and metabolism, mineral levels can improve the body can regulate glucose metabolism in human diabetes; tea can be a diuretic, and enhance renal excretory function; tea prevents aging,mac eye shadows, coronary heart disease prevention and control; tea can be clearly projects, anti-inflammatory, detoxification, reducing stomach fire, resistance to radiation damage and anti-cancer effect. Iron Goddess of Mercy and which products best green tea; grapefruit: clearing away heat; cooked green bean soup.
Chinese medicine, salt, there is heat, cooling blood, the role of detoxification. According to the Therefore, the early morning wake up drink a glass of water fasting is conducive to Reduce Pathogenic Fire kidney, maintaining smooth stool, improve digestion and absorption of gastrointestinal function.
honey fill in, dryness, pain relief, detoxification role, used to treat weak stomach, indigestion, Dryness of dry cough, dry constipation and other intestinal diseases. Modern medical research has proved that honey contains glucose, vitamins and phosphorus, calcium, substances that can regulate the nervous system disorders, which play to increase appetite and promote the role of sleep. So every day before going to bed to take 10-20 ml of honey with warm water transfer service, not only spleen and stomach, replenishing qi and blood, as well as calm, soothe the nerves, Chufan role. However, the time to drink salt water and honey also pay attention to: salt contains a lot of sodium, can cause high blood pressure. Thus, lower salt concentration, salt content of 100 ml of water is best not to over 0.9 grams. Acute nephritis, liver cirrhosis, ascites, edema, preferably in plain water instead, should not increase the burden on the kidneys and heart. Higher sugar content in honey, diabetes patients should not take it.
In addition, the salt water and honey drink must be combined because the two are complementary. High content of potassium in honey, helps flush the body of excess sodium.
(1)解析：f(x)=x^2+x-1=0，α=(-1+√5)/2, β=(-1-√5)/2
(2)证明：设a1=1, a(n+1)=an-f(an)÷f"(an)(n=1.2.3...)
a(n+1)=[(an)^2+1]/[2an+1]
设g(x)=(x^2+1)/(2x+1)
令g’(x)=2(x^2+x-1)/(2x+1)^2=0
X1=α>0, x2=β<0
∵g’’(x1)>0,∴函数g(x)在x1处取极小值g(α)=α≈0.618
∴当x>α时，函数g(x)单调增
∴当x=n (n∈N+)时，g(x)> α
即对任意的正整数n都有an＞α成li
所以对任意的正整数都可以成立的
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