Chung minh A= x/y+z+t =y/z+t+x = z/t+x+y = t/x+y+z la so nguyen.
Những câu hỏi liên quan
cho x/y+z+t=y/z+t+x=z/t+x+y=t/x+y+z
chung minh bieu thuc sau co gia tri nguyen
p=(x+y/z+t)+(y+z/t+x)+(z+t/x+y)+(t+x/y+z)
Tim so nguyen x , y, z , t biet : 38 * ( x * y * z * t + x * y + x * t + z * t + 1 ) = 49 * ( y * z * t + y +t )
A = ( x+y)-(z+t)
B = ( x-z)+(y-t)
( A va B la hai so nguyen, so sanh A va B)
A = B
Ta có: A = ( x + y ) - ( z + t ) = x + y - z - t
B = ( x - z ) + ( y - t ) = x - z + y - t = x + y - z - t = A
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cho x/y+z+t=y/z+t+x=z/t+x+y=t/x+y+z cmr bieu thuc sau co gia tri nguyen P=(x+y/z+t)+(y+z/t+x)+(z+t/x+y)=(t+x/y+z)
cho x/(y+z+t)=y/(z+t+x)=z/(t+x+y)=t/(x+y+z)
cmr bieu thuc sau co gia tri nguyen
P=(x+y)/(z+t)+(y+z)/(t+x)+(z+t)/(x+y)+(t+x)/(y+z)
cho x/y=y/z/=z/t .chung minh rang:(x+y+z/y+z+t)^3=x/t
Áp dụng tính chất dãy tỉ số bằng ngau ta có :
\(\dfrac{x}{y}=\dfrac{y}{z}=\dfrac{z}{t}=\dfrac{x+y+z}{y+z+t}\)
\(\Rightarrow\dfrac{x.y.z}{y.z.t}=(\dfrac{x+y+z}{y+z+t})^3\)
\(\Rightarrow\dfrac{x}{t}=(\dfrac{x+y+z}{y+z+t})^3\)
\(\Rightarrowđpcm\)
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cho x,y,z la cac so nguyen duong va x+y+z la so le, cac so thuc a,b,c thoa man (a-b)/x=(b-c)/y=(a-c)/z. chung minh rang a=b=c
cho x, y , z la cac so nguyen thoa man x . y - x. z + y.z - z^2 +1 =0 chung minh rang x+ y =0
cho x,y,z la cac so thuc thoa x+y+z=0, x+1>0, y+1>0, z+1>0. tim GTLN cua P=\(\frac{x}{x+1}+\frac{y}{y+1}+\frac{z}{z+4}\)
cho x,y,z,t la cac so duong. tim GTNN cua A=\(\frac{x-t}{t+y}+\frac{t-y}{y+z}+\frac{y-z}{z+x}+\frac{z-x}{x+t}\)