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eduard
3 years ago
12

The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1 : 4, 3 : 2 and 3 : 7 respectively. Show that

there exists a point G such that the sum of the vectors AD, BE, CF is parallel to CG. What ratio does G divide AB?
Mathematics
1 answer:
Slav-nsk [51]3 years ago
5 0

Answer:

ac = d + liga

Step-by-step explanation:

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Make a substitution:

\begin{cases}u=2x+y\\v=2x-y\end{cases}

Then the system becomes

\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}

Simplifying the equations gives

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\implies\dfrac uv=\pm27

\implies u=\pm27v

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8 0
3 years ago
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