book Maths Puzzle Numerical Ability

Let T be a linear operator in V. Prove that T^2 = 0 if and only if the range T is a subset of null T.

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Ive been trying to work on this problem forever and now i need some help.
The problem is:
Two friends are 60 miles apart. They decide to ride their bicycles to meet each other. S
twice the sum of 4 and some number is 34 what is the number
could some please help i am stuck thank you mike