Đáp án:
Ta có :
$\dfrac{15}{x - 9}$ = $\dfrac{20}{y - 12}$ = $\dfrac{40}{z - 24}$
=> $\dfrac{x - 9}{15}$ = $\dfrac{y - 12}{20}$ = $\dfrac{z - 24}{40}$
=> $\dfrac{x}{15}$ - $\dfrac{9}{15}$ = $\dfrac{y}{20}$ - $\dfrac{12}{20}$ = $\dfrac{z}{40}$ - $\dfrac{24}{40}$
Do $\dfrac{9}{15}$ = $\dfrac{12}{20}$ = $\dfrac{24}{40}$ = $\dfrac{3}{5}$
=> $\dfrac{x}{15}$ = $\dfrac{y}{20}$ = $\dfrac{z}{40}$
=>$\dfrac{x^2}{15^2}$ = $\dfrac{y^2}{20^2}$ = $\dfrac{z^2}{40^2}$ = $\dfrac{x.y}{15.20}$ =$\dfrac{1200}{300}$ $= 4 = 2^2$
$ => x^2 = 2^2 . 15^2 = (2.15)^2 = 30^2 => x = ± 30$
$ => y^2 = 2^2 . 20^2 = ( 2 . 20)^2 = 40^2 => y = ± 40$
$ => z^2 = 2^2 . 40^2 = ( 2 . 40)^2 = 80^2 => z = ± 80$
Do x,y,z cùng dấu
=> \(\left[ \begin{array}{l}x=30;y=40;z=80\\x=-30;y=-40;z=-80\end{array} \right.\)
Giải thích các bước giải:
