Specimen Cyprus Seniors Provincial/2nd grade/Problems
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[hide]Problem 1
Let be a parallelogram. Let be a straight line passing through without cutting . If are the projections of on respectively, show that
a) the distance of from is equal to the sum of the distances $\Beta, \Delta$ (Error compiling LaTeX. Unknown error_msg) from .
b) .
Problem 2
If ,, and prove that
Problem 3
Prove that if are positive integers, then the equation has irrational roots.
Problem 4
If are the roots of equation then:
a) Prove that and
b) Calculate the value of: .