Toán Lớp 7: Tìm x, y, z thuộc Q: I x-3/4 I + I 2/5-y I + I x-y+z I=0

Question

Toán Lớp 7:  Tìm x, y, z thuộc Q: I x-3/4 I + I 2/5-y I + I x-y+z I=0

ngoclandiep · Answer

Ta c&oacute;: |x - 3/4| &ge; 0 &forall; x   |2/5 - y| &ge; 0 &forall; y   |x - y + z| &ge; 0 &forall; z   &rArr; |x - 3/4| + |2/5 - y| + |x - y + z| &ge; 0 &forall; x, y, z.   Dấu '=' xảy ra &hArr; {(x - 3/4 = 0),(2/5 - y = 0),(x - y + z = 0):}.   &hArr; {(x = 3/4),(y = 2/5):}.   m&agrave; x - y + z = 0   &rArr; z = 0 - (3/4 + 2/5) = -7/20   Vậy x = 3/4; y = 2/5; z = -7/20.

landinhngoc97 · Answer

***Lời giải***

Ta có:| x-3/4 | , | 2/5-y | ,| x-y+z |≥0
=>| x-3/4 | + | 2/5-y | +| x-y+z |≥0
Mà | x-3/4 | + | 2/5-y | +| x-y+z |=0

=>$\begin{cases} x-\dfrac{3}{4}=0\\\dfrac{2}{5}-y=0\\x-y+z=0 \end{cases}$
<=>$\begin{cases} x=\dfrac{3}{4}\\y=\dfrac{2}{5}\\\dfrac{3}{4}-\dfrac{2}{5}+z=0 \end{cases}$
<=>$\begin{cases} x=\dfrac{3}{4}\\y=\dfrac{2}{5}\\\dfrac{7}{20}+z=0 \end{cases}$
<=>$\begin{cases} x=\dfrac{3}{4}\\y=\dfrac{2}{5}\\z=-\dfrac{7}{20} \end{cases}$

Vậy (x;y;z)=(3/4;2/5;-7/20)