cho a,b > 0 va a + b = 1 . Tim GTNN cua 1/a^3+ab+b^3 + 4.a^2.b^2+1/ab
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cho a,b > 0 va a + b = 1 . Tim GTNN của
\(\dfrac{1}{a^3}+ab+b^3+4a^2b^2+\dfrac{1}{ab}\)
Cho 2 so thuc a va b thoa màn a>b va ab=4. Tim GTNN cua bieu thuc P=(a2+b2+ 1):(a-b)
Cho a,b>0,a+b=1.Tim GTNN cua A=\(\frac{3}{a^2+b^2}+\frac{2}{ab}\)
\(A=\frac{3}{a^2+b^2}+\frac{2}{ab}\)
\(=\frac{3}{a^2+b^2}+\frac{4}{2ab}\ge\frac{\left(\sqrt{3}+2\right)^2}{\left(a+b\right)^2}\)(cauchy-schwarz dạng engel)
\(=7+4\sqrt{3}\)
Cho a,b>0 va a+b nho hon hoac bang 1. Tim GTNN \(S=\frac{1}{a^3+b^3}+\frac{1}{a^2b}+\frac{1}{ab^2}\)
1, tim GTLN cua A=13/(x+5)^2+7
2, tim GTNN cua B=|x+2017|+(y+3)^2+2017
3, cho a-1/2=b+3/4=c-5/6 va 5a-3b-4c=46. Tim a,b,c.
Cho a>0 b>0 va a+b =< 4 . tim GTNN cua bkeu thuc A=2/(a^+b^2) +35/ab+2ab
\(A=\frac{2}{a^2+b^2}+\frac{35}{ab}+2ab\)
\(=\frac{2}{a^2+b^2}+\frac{2}{2ab}+\frac{32}{ab}+2ab+\frac{2}{ab}\)
\(\ge\frac{2\sqrt{2^2}}{\left(a+b\right)^2}+2\sqrt{\frac{32}{ab}\cdot2ab}+\frac{2}{\frac{\left(a+b\right)^2}{4}}\)
\(\ge\frac{1}{2}+2\cdot8+\frac{1}{2}=17\)
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cho a>0,b>0 va a+b<=1. tim gtnn cua a^2+b^2+1/a^2+1/b^2
Ta co:\(1\ge a+b\ge2\sqrt{ab}\Rightarrow ab\le\frac{1}{4}\)
Dat \(P=a^2+b^2+\frac{1}{a^2}+\frac{1}{b^2}\)
\(=a^2+\frac{1}{16a^2}+b^2+\frac{1}{16b^2}+\frac{15}{16}\left(\frac{1}{a^2}+\frac{1}{b^2}\right)\)
\(=a^2+\frac{1}{16a^2}+b^2+\frac{1}{16b^2}+\frac{15}{16}.\frac{a^2+b^2}{a^2b^2}\ge\frac{1}{2}+\frac{1}{2}+\frac{15}{16}.\frac{2}{ab}\ge1+\frac{15}{16}.\frac{2}{\frac{1}{4}}=\frac{17}{2}\)
Dau '=' xay ra \(a=b=\frac{1}{2}\)
Vay \(P_{min}=\frac{17}{2}\)khi \(a=b=\frac{1}{2}\)
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Bai 1: a)Tim so tu nhien a biet 1960va2002 chia cho a cung co so du la 28b)Tim 2 sop tu nhien a va b , biet :BCNN(a,b)300;UCLN(a,b)15 va a+15bBai 2:a)Tong sau la binh phuong so nao ?S1+3+5+7+...+199b) Cho so ab va so ababab 1)chung to ababab la boi cua ab2)So 3 va 10101 co phai la uoc cua ababab khong , vi sao?Bai 3a)Hay viet them dang sau so 664 ba chu so de nhan duoc sdo co 6 chu so chia het cho 5,9,11b)Tim so nguyen x thuoc Z biet rang :(x^2-1)(x^2-4)0Bai 4 :tim so nguyen x va y biet: xy-x+2...
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Bai 1: a)Tim so tu nhien a biet 1960va2002 chia cho a cung co so du la 28
b)Tim 2 sop tu nhien a va b , biet :BCNN(a,b)=300;UCLN(a,b)=15 va a+15=b
Bai 2:a)Tong sau la binh phuong so nao ?
S=1+3+5+7+...+199
b) Cho so ab va so ababab
1)chung to ababab la boi cua ab
2)So 3 va 10101 co phai la uoc cua ababab khong , vi sao?
Bai 3
a)Hay viet them dang sau so 664 ba chu so de nhan duoc sdo co 6 chu so chia het cho 5,9,11
b)Tim so nguyen x thuoc Z biet rang :
(x^2-1)(x^2-4)<0
Bai 4 :tim so nguyen x va y biet: xy-x+2y=3
cho a,b>0(a+b<=1) tim GTNN cua J=\(\frac{1}{a^2+b^2}+\frac{1}{ab}\)
\(J=\frac{1}{a^2+b^2}+\frac{1}{2ab}+\frac{1}{2ab}\ge\frac{4}{a^2+b^2+2ab}+\frac{1}{\frac{2\left(a+b\right)^2}{4}}=\frac{6}{\left(a+b\right)^2}\ge6\)
\(\Rightarrow J_{min}=6\) khi \(a=b=\frac{1}{2}\)
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