Question

Đã trả lời bởi chuyên gia

Answer 1

\[\begin{array}{l}
a)\frac{a}{2} = \frac{b}{3} = \frac{c}{4}\\
= > \frac{a}{2} = \frac{{2b}}{6} = \frac{{3c}}{{12}}
\end{array}\]

Áp dụng tính chất dãy tỉ số bằng nhau:

\[\begin{array}{l}
\frac{a}{2} = \frac{{2b}}{6} = \frac{{3c}}{{12}} = \frac{{a + 2b - 3c}}{{2 + 6 - 12}} = \frac{{ - 20}}{{ - 4}} = 5\\
= > \frac{a}{2} = 5 = > a = 10\\
\frac{{2b}}{6} = 5 = > b = 15\\
\frac{{3c}}{{12}} = 5 = > c = 20\\
vay:\left( {a;b;c} \right) = \left( {10;15;20} \right)
\end{array}\]

\[\begin{array}{l}
b)\frac{a}{2} = \frac{b}{3}\\
= > a = \frac{2}{3}b\\
,\frac{b}{5} = \frac{c}{4}\\
= > c = \frac{4}{5}b\\
\;\;a - b + c = - 49\\
= > \frac{2}{3}b - b + \frac{4}{5}b = - 49\\
= > \frac{7}{{15}}b = - 49\\
= > b = - 105\\
= > a = \left( { - 105} \right).\frac{2}{3} = - 70\\
= > c = \left( { - 105} \right).\frac{4}{5} = - 84\\
vay:\left( {a;b;c} \right) = \left( { - 70; - 105; - 84} \right)
\end{array}\]

\[\begin{array}{l}
c)\frac{a}{2} = \frac{b}{3} = \frac{c}{4}\;\;\\
= > a = \frac{2}{3}b;c = \frac{4}{3}b\\
{a^2} - {b^2} + 2.{c^2}\; = 108\\
= > {\left( {\frac{2}{3}b} \right)^2} - {b^2} + 2.{\left( {\frac{4}{3}b} \right)^2} = 108\\
= > 3{b^2} = 108\\
= > {b^2} = 36\\
= > b = \pm 6\\
+ )b = - 6\\
= > a = \frac{2}{3}\left( { - 6} \right) = - 4\\
c = \frac{4}{3}\left( { - 6} \right) = - 8\\
+ )b = 6\\
= > a = \frac{2}{3}.6 = 4\\
c = \frac{4}{3}.6 = 8\\
vay:\left( {a;b;c} \right) = \left( { - 4; - 6; - 8} \right);\left( {4;6;8} \right)
\end{array}\]

...Xem thêm

Answer 2

\[\begin{array}{l}
a)\frac{a}{2} = \frac{b}{3} = \frac{c}{4}\\
= > \frac{a}{2} = \frac{{2b}}{6} = \frac{{3c}}{{12}}
\end{array}\]

Áp dụng tính chất dãy tỉ số bằng nhau:

\[\begin{array}{l}
\frac{a}{2} = \frac{{2b}}{6} = \frac{{3c}}{{12}} = \frac{{a + 2b - 3c}}{{2 + 6 - 12}} = \frac{{ - 20}}{{ - 4}} = 5\\
= > \frac{a}{2} = 5 = > a = 10\\
\frac{{2b}}{6} = 5 = > b = 15\\
\frac{{3c}}{{12}} = 5 = > c = 20\\
vay:\left( {a;b;c} \right) = \left( {10;15;20} \right)
\end{array}\]

\[\begin{array}{l}
b)\frac{a}{2} = \frac{b}{3}\\
= > a = \frac{2}{3}b\\
,\frac{b}{5} = \frac{c}{4}\\
= > c = \frac{4}{5}b\\
\;\;a - b + c = - 49\\
= > \frac{2}{3}b - b + \frac{4}{5}b = - 49\\
= > \frac{7}{{15}}b = - 49\\
= > b = - 105\\
= > a = \left( { - 105} \right).\frac{2}{3} = - 70\\
= > c = \left( { - 105} \right).\frac{4}{5} = - 84\\
vay:\left( {a;b;c} \right) = \left( { - 70; - 105; - 84} \right)
\end{array}\]

\[\begin{array}{l}
c)\frac{a}{2} = \frac{b}{3} = \frac{c}{4}\;\;\\
= > a = \frac{2}{3}b;c = \frac{4}{3}b\\
{a^2} - {b^2} + 2.{c^2}\; = 108\\
= > {\left( {\frac{2}{3}b} \right)^2} - {b^2} + 2.{\left( {\frac{4}{3}b} \right)^2} = 108\\
= > 3{b^2} = 108\\
= > {b^2} = 36\\
= > b = \pm 6\\
+ )b = - 6\\
= > a = \frac{2}{3}\left( { - 6} \right) = - 4\\
c = \frac{4}{3}\left( { - 6} \right) = - 8\\
+ )b = 6\\
= > a = \frac{2}{3}.6 = 4\\
c = \frac{4}{3}.6 = 8\\
vay:\left( {a;b;c} \right) = \left( { - 4; - 6; - 8} \right);\left( {4;6;8} \right)
\end{array}\]

1 câu trả lời 465

Câu hỏi hot cùng chủ đề

Bài viết mới nhất Lớp 7