tìm x, y, z biết 3|x|+5/3=3|y|-1/5=3-z/7 và 2|x|+7|y|+3z=-14 10/11/2021 Bởi Jade tìm x, y, z biết 3|x|+5/3=3|y|-1/5=3-z/7 và 2|x|+7|y|+3z=-14
Giải thích các bước giải: Ta có: $3|x|+\dfrac53=3-\dfrac{z}{7}$ $\to 3|x|=\dfrac{12}{5}-\dfrac{z}{7}$ $\to |x|=\dfrac13(\dfrac{12}{5}-\dfrac{z}{7})$ Lại có $3|y|-\dfrac15=3-\dfrac{z}{7}$ $\to 3|y|=\dfrac{16}{5}-\dfrac{z}{7}$ $\to |y|=\dfrac13(\dfrac{16}{5}-\dfrac{z}{7})$ Lại có $2|x|+7|y|+3z=-14$ $\to 2\cdot \dfrac13(\dfrac{12}{5}-\dfrac{z}{7})+7\cdot \dfrac13(\dfrac{16}{5}-\dfrac{z}{7})+3z=-14$ $\to \dfrac{18z}{7}+\dfrac{136}{15}=-14$ $\to z=-\dfrac{1211}{135}$ $\to |x|=\dfrac13(\dfrac{12}{5}-\dfrac{-\dfrac{1211}{135}}{7})=\dfrac{497}{405}$ $\to x=\pm\dfrac{497}{405}$ Lại có: $|y|=\dfrac13(\dfrac{16}{5}-\dfrac{-\dfrac{1211}{135}}{7})=\dfrac{121}{81}$ $\to y=\pm\dfrac{121}{81}$ Bình luận
Giải thích các bước giải:
Ta có:
$3|x|+\dfrac53=3-\dfrac{z}{7}$
$\to 3|x|=\dfrac{12}{5}-\dfrac{z}{7}$
$\to |x|=\dfrac13(\dfrac{12}{5}-\dfrac{z}{7})$
Lại có $3|y|-\dfrac15=3-\dfrac{z}{7}$
$\to 3|y|=\dfrac{16}{5}-\dfrac{z}{7}$
$\to |y|=\dfrac13(\dfrac{16}{5}-\dfrac{z}{7})$
Lại có $2|x|+7|y|+3z=-14$
$\to 2\cdot \dfrac13(\dfrac{12}{5}-\dfrac{z}{7})+7\cdot \dfrac13(\dfrac{16}{5}-\dfrac{z}{7})+3z=-14$
$\to \dfrac{18z}{7}+\dfrac{136}{15}=-14$
$\to z=-\dfrac{1211}{135}$
$\to |x|=\dfrac13(\dfrac{12}{5}-\dfrac{-\dfrac{1211}{135}}{7})=\dfrac{497}{405}$
$\to x=\pm\dfrac{497}{405}$
Lại có:
$|y|=\dfrac13(\dfrac{16}{5}-\dfrac{-\dfrac{1211}{135}}{7})=\dfrac{121}{81}$
$\to y=\pm\dfrac{121}{81}$