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In a triangle AC median AD is produced to X such that AD=DX . prove that ADXC is a parallelogram

It should be ABXC is a parallelogram


I am sure you meant, in triangle ABC.
and i hope you have the figure with you.

Since AD is the median,
also AD=DX is given.
So the diagonals are bisecting each other :)
Thats the property of a parallelogram!

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In the quadrilateral ABXC
AD = DX   (given)
BD = DC (As AD is median and D is the midpoint of BC)

diagonals BC and AX are bisecting each other.

Therefore, ABXC is a parallelogram.
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