cho biet a,b,c >0 dieu kien \(a^2+b^2+c^2=1\)Tinh GTNN cua bieu thuc A = \(\frac{ab}{c}+\frac{bc}{a}+\frac{ac}{b}\)
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cho a,b,c >0 thoa man dieu kien a^2 +b^2 +c^2 = 1
tinh gia tri nho nhat cua bieu thuc A= ab/c + bc/a + ca/b
Cho 3 so a,b,c thoa man dieu kien abc=105 va bc+b+1\(\ne\) 0 .
Tinh gia tri cua bieu thuc :
\(S=\frac{105}{abc+ab+a}+\frac{b}{bc+b+1}+\frac{a}{ab+a+105}\)
day du se like , ko neu cau hoi tuong tu
Vì abc=105
=> \(S=\frac{abc}{abc+ab+a}+\frac{b}{bc+b+1}+\frac{a}{ab+a+abc}\)
\(=\frac{abc}{a\left(bc+b+1\right)}+\frac{b}{bc+b+1}+\frac{a}{a\left(b+1+bc\right)}\)
\(=\frac{bc}{bc+b+1}+\frac{b}{bc+b+1}+\frac{1}{bc+b+1}\)
\(=\frac{bc+b+1}{bc+b+1}=1\)
Vậy S=1.
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Cho 2 so thuc a, b thoa man dieu kien ab= 1, a+ b\(\ne\)0. Tinh gia tri bieu thuc :
P= \(\frac{1}{\left(a+b\right)^3}\left(\frac{1}{a^3}+\frac{1}{b^3}\right)+\frac{3}{\left(a+b\right)^4}\left(\frac{1}{a^2}+\frac{1}{b^2}\right)+\frac{6}{\left(a+b\right)^3}\left(\frac{1}{a}+\frac{1}{b}\right)\)
biet ab-ac+bc=c^2-1 tinh gia tri bieu thuc b=\(\frac{a}{b}\)
\(ab-ac+bc=c^2-1\)
\(ab-ac+bc-c^2=-1\)
\(a\left(b-c\right)+c\left(b-c\right)=-1\)
\(\Leftrightarrow\left(a+c\right)\left(b-c\right)=-1\)
=> a + c = 1 thì b - c = - 1; a + c = - 1 thì b - c = 1 => a + c và b - c đối nhau
\(\Rightarrow a+c=-\left(b-c\right)\)
\(a+c=-b+c\)
\(\Rightarrow a=-b\)
\(\Rightarrow B=\frac{a}{b}=-1\)
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Bai 1)Cho bieu thuc Afrac{x+y-2sqrt{xy}}{x-y}a)Tim dieu kien de A co nghiab)Rut gon Ac)Tinh A biet x3+2sqrt{2}va y3-2sqrt{2}Bai 2) Cho bieu thuc Bfrac{x-3}{sqrt{x-1}-sqrt{2}}a)Tim dieu kien de B co nghiab)Rut gon Bc) Tinh B voi x4left(2-sqrt{3}right)d)Tim x de B co gia tri nho nhat
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Bai 1)Cho bieu thuc A=\(\frac{x+y-2\sqrt{xy}}{x-y}\)
a)Tim dieu kien de A co nghia
b)Rut gon A
c)Tinh A biet x=\(3+2\sqrt{2}\)va y=\(3-2\sqrt{2}\)
Bai 2) Cho bieu thuc B=\(\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\)
a)Tim dieu kien de B co nghia
b)Rut gon B
c) Tinh B voi x=\(4\left(2-\sqrt{3}\right)\)
d)Tim x de B co gia tri nho nhat
a) A có nghĩa\(\Leftrightarrow x-y\ne0\Leftrightarrow x\ne y\)
b) \(A=\frac{x+y-2\sqrt{xy}}{x-y}=\frac{\left(\sqrt{x-\sqrt{y}}\right)^2}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}=\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\)
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cho bieu thuc A=\(\frac{x^2+3}{x-2}\)
tim dieu kien cua x de gia tri cua bieu thuc A
a,A<0
b, A nhan gia tri nguyen
a) \(A< 0\Leftrightarrow\frac{x^2+3}{x-2}< 0\)
Mà \(x^2+3>0\Rightarrow x-2< 0\Leftrightarrow x< 2\)
b) \(A\inℤ\Leftrightarrow\frac{x^2+3}{x-2}\in Z\)
Ta có \(\frac{x^2+3}{x-2}=\frac{\left(x^2-4x+4\right)+\left(4x-8\right)+7}{x-2}\)
\(=x-2+4+\frac{7}{x-2}\)
\(\Rightarrow\frac{x^2+3}{x-2}\in Z\Leftrightarrow7⋮\left(x-2\right)\)
\(\Rightarrow x-2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow x\in\left\{3;1;9;-5\right\}\)
cho a,b,c la ba so thuc duong thoa man dieu kien a+b+c=1
chung minh rang P=\(\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ca}{b+ca}}\le\frac{3}{2}\)
lấy bút xóa mà xóa hết là khỏe
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tinh gia tri cua bieu thuc A=\(\left(\frac{a-b}{c}+\frac{b-c}{a}+\frac{c-a}{b}\right)\))\(\left(\frac{c}{a-b}+\frac{a}{b-c}+\frac{b}{c-a}\right)\). cho biet a+b+c=0
Cho a,b,c là cac so thoa man dieu kien \(\frac{2a-b}{a+b}=\frac{b-c+a}{2a-b}=\frac{2}{3}\)
Khi đo gia tri cua bieu thuc \(P=\frac{\left(5b+4a\right)^5}{\left(5b+4c\right)^2.\left(a+3c\right)^3}\)