Đáp án+Giải thích các bước giải:
i, $\dfrac{x}{2}$ = $\dfrac{y}{3}$ = $\dfrac{2}{5}$ = $\dfrac{x+y+2}{2+3+5}$ = $\dfrac{30}{10}$ = 3.
$\Rightarrow$ $\begin{cases} x=6\\y=9\\z=15 \end{cases}$
ii, $\dfrac{x}{2}$ = $\dfrac{2y}{6}$ = $\dfrac{3z}{15}$ = $\dfrac{x-2y+3z}{2-6+15}$ = $\dfrac{22}{11}$ = 2
$\Rightarrow$ $\begin{cases} x=4\\y=6\\z=10 \end{cases}$
iii, $\dfrac{x}{2}$ = $\dfrac{y}{3}$ = $\dfrac{2}{5}$ = t
$\Rightarrow$ t³ = $\dfrac{x.y.z}{2.3.5}$ = $\dfrac{-240}{30}$ = -8
$\Rightarrow$ t = -2
$\Rightarrow$ $\begin{cases} x=-4\\y=-6\\z=-10 \end{cases}$
iv, $\dfrac{x²}{4}$ = $\dfrac{y²}{9}$ = $\dfrac{z²}{25}$
$\Rightarrow$ $\dfrac{x²}{4}$ = $\dfrac{3y²}{27}$ = $\dfrac{2²}{25}$ = $\dfrac{x²+3y²-2²}{4+27-25}$ = $\dfrac{150}{6}$ = 25
$\Rightarrow$ $\begin{cases} x=10\\y=15\\z=25 \end{cases}$
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