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cho các số z,y,z thỏa mãn :\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)và 2x+3y-z=95. khi đó x+y+z=
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)+3\left(y-2\right)-\left(z-3\right)}{2.2+3.3-4}=\frac{95-5}{9}=10\)
x-1 =20 => x =21
y-2 =30 => y =32
z-3 =40 => z =43
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2x-2+3y-6-z+3}{4+9-4}=\frac{90}{9}=10\)
\(\Rightarrow\) x - 1 = 20; y - 2 = 30; z - 3 = 40
\(\Rightarrow\) x = 21; y = 32; z = 43
Cho các số x;y;x thỏa mãn: \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) và 2x+3y-z=95 Khi đó x+y+z=
Áp dụng tính chất dãy tỉ số bằng nhau , ta có:
x - 1/2 = y - 2/3 = z-3/4 = 2x - 2 + 3y - 6 - z + 3/4 + 9 - 4 = 95 + -5/10 = 10
x-1/2 = 10 => x =21
y-2/3 =10 => y = 32
z-3/4 = 10 => z = 43
Vậy x + y + z = 21 + 32 + 43 = 96
Ta có: \(\frac{x-1}{2}=\frac{2x-2}{4};\frac{y-2}{3}=\frac{3y-6}{9};\frac{z-3}{4}=\frac{-z+3}{-4}\)
Vì \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\)nên \(\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{-z+3}{-4}=\frac{2x-2+3y-6-z+3}{4+9+\left(-4\right)}=\frac{50-5}{9}=\frac{45}{9}=5\)
\(\Rightarrow\frac{x-1}{2}=5\Rightarrow x=11\)
\(\Rightarrow\frac{y-2}{3}=5\Rightarrow y=17\)
\(\Rightarrow\frac{z-3}{4}=5\Rightarrow z=23\)
Vậy, \(x+y+z=11+17+23=51\)
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)}{4}=\frac{3\left(y-2\right)}{9}=\frac{2x-2}{4}=\frac{3y-6}{9}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{\left(2x-2\right)+\left(3y-6\right)-\left(z-3\right)}{4+9-4}=\frac{\left(2x+3y-z\right)-5}{9}=\frac{50-5}{9}=\frac{45}{9}=5\)
=> \(\frac{x-1}{2}=5\Rightarrow x=11\)
\(\frac{y-2}{3}=5\Rightarrow y=17\)
\(\frac{z-3}{4}=5\Rightarrow z=23\)
Vậy x = 11 ; y = 17 ; z = 23
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\Rightarrow\frac{2x-1}{4}=\frac{3y-2}{9}=\frac{z-3}{4}\) vaf 2x+3y-z=50
Ap dung tinh chat day ti so bang nhau , ta co :
\(\frac{2x-1}{4}=\frac{3y-2}{9}=\frac{z-3}{4}=\frac{2x+3y-z-1-2-3}{4+9-4}=\frac{50-\left(-4\right)}{9}=-\frac{54}{9}=-6\)
Suy ra : \(\frac{2x-1}{4}=-6\Rightarrow2x-1=-6.4=-24\Rightarrow x-1=-24:2=-12\Rightarrow x=-12+1=-11\)
\(\frac{3y-2}{9}=-6\Rightarrow3y-2=-6.9=-54\Rightarrow y-2=-54:3=-18\Rightarrow y=-18+\left(-2\right)=-20\)
\(\frac{z-3}{4}\Rightarrow z-3=4.3=12\Rightarrow z=12+3=15\)
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2\left(x-1\right)}{4}=\frac{3\left(y-2\right)}{9}=\frac{2x-2+3y-6-z+3}{4+9-4}=\frac{2x+3y-z-5}{9}=\frac{90}{9}=10\)
=> x-1 = 10.2 = 20 => x= 21
y-2 = 10.3 = 30 => y = 32
z-3 = 10.4 =40 => z = 43
Ta có:\(\frac{x-1}{2}=\frac{2.\left(x-1\right)}{2.2}=\frac{2x-2}{4}\)
\(\frac{y-2}{3}=\frac{3.\left(y-2\right)}{3.3}=\frac{3y-6}{9}\)
Theo t/c dãy tỉ số = nhau:
\(\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z-3}{4}=\frac{2x-2+3y-6-z+3}{4+9-4}=\frac{2x+3y-z-5}{9}=\frac{95-5}{9}=\frac{90}{9}=10\)
=> \(\frac{x-1}{2}=10\Rightarrow x-1=10.2=20\Rightarrow x=20+1=21\)
=> \(\frac{y-2}{3}=10\Rightarrow y-2=10.3=30\Rightarrow y=30+2=32\)
=> \(\frac{z-3}{4}=10\Rightarrow z-3=10.4=40\Rightarrow z=40+3=43\)
Vậy x + y + z = 21 + 32 + 43 = 96.