A=(√a+1/√a-1 - √a-1/√a+1 + 4√a)(√a+1/√a) voi a>0, a khac 1
Những câu hỏi liên quan
Chung to rang 1/a=1/a+1+1/a*(a+1) voi a thuoc so nguyen , a khac 0, a khac -1
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bai thi .....................kho..........................kho..............troi.................thilanh.............................ret..................wa.........................dau................wa......................tich....................ung.....................ho.....................cho............do.................lanh
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chung to rang 1/a =1/a+1=1/a(a+1) voi thuoc Z , a khac 0 va -1
Cho 1 so nguyen a khac 0. So sanh -a voi a,-a voi 0
Cho a la so tu nhien khac 0.So sanh a/a+1+a+1/a voi 2
Bài làm:
Ta có: Xét bất đẳng thức sau:
\(\left(x-y\right)^2\ge0\left(\forall x\right)\)\(\Rightarrow x^2-2xy+y^2\ge0\)
\(\Leftrightarrow x^2+2xy+y^2\ge4xy\)
\(\Leftrightarrow\left(x+y\right)^2\ge4xy\Leftrightarrow x+y\ge2\sqrt{xy}\)
Áp dụng bất đẳng thức trêm vào biểu thức:
\(\frac{a}{a+1}+\frac{a+1}{a}\ge2\sqrt{\frac{a}{a+1}.\frac{a+1}{a}}=2.1=2\)
\(\Rightarrow\frac{a}{a+1}+\frac{a+1}{a}\ge2\)
Học tốt!!!!
Cho a,b,c khac nhau va khac 0 : a+1/b=b+1/c=c+1/a=k
CMR: k=1 hoac -1
LAM ON GIUP EM BAI NAY VOI !!!!!!!!!!!!
Cho 1/c=1/2(1/a+1/b)(voi a,b,ckhac 0; b khac c). CMRa/b=a-c/c-b
tim 1 so tu nhien a khac 1 va 1 so tu nhien n khac 1 sao cho khi nhan a voi n duoc 1 so hon a 59 don vi
Ta có :
a x n - a = 59
n ; a \(\ne1\)
a x ( n - 1 ) = 59
=> a hoặc n = 59
Ta chọn
a = 59 ; nếu a = 59 thì n - 1 = 1 ; n = 2
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Giai va bien luan cac phuong trinh sau:
1. \(\frac{a+b-x}{c}+\frac{a+c-x}{b}+\frac{b+c-x}{a}+\frac{4x}{a+b+c}=1\)
(an x) voi dk; a,b,b khac 0 va a+b+c khac 0
2.\(\frac{x-a}{bc}+\frac{x-b}{ac}+\frac{x-c}{ab}=2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
(an x) voi dk: a,b,c khac 0
3, \(\frac{mx+3}{6}+\frac{m^2-1}{2}=\frac{x+5}{10}+\frac{2}{5}\left(x+m^2+1\right)\)
(an x)
Cho minh hoi bai nay. Chi can tra loi 1 cau cung duoc! Tick cho ai tra loi som nhat, day du nhat.
1. Cho so huu ti y=2a-1/-3. Voi gia tri nao cua a thi y la so duong, y la so am, khong phai so duong cung phai so am?
2. Cho so huu ti x=a-5/a (a khac 0). Voi gia tri nao cua a thi x la so nguyen?
3. Cho so huu ti x=a-3/2a (a khac 0). Voi gia tri nao cua a thi x la so nguyen?