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Let x,y,z be positive integers such that...

Let x,y,z be positive integers such that HCF(x,y,z)=1 and `x^(2)+y^(2)=2z^(2)`. Which of the following statements are true ?
I. 4 divides x or 4 divides y.
II. 3 divides x+y or 3 divides x-y
III. 5 divides `z(x^(2-y^(2)))`

A

I and II only

B

II and III only

C

II only

D

III only

Text Solution

Verified by Experts

The correct Answer is:
B
Take combination such as x=1,y=7,z=5
Now, check option
(ii) & (iii) statement are correct.
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