Let x,y,z be positive integers such that HCF (x,y,z) = 1 and x2 + y2 =

1.	Let x,y,z be positive integers such that HCF (x,y,z) = 1 and x2 + y2 = 2z2 . 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(x2 – y2)(A) I and II only(B) II and III only(C) II only(D) III only
Answer» Correct option (B) II and III only Explanation: Take combination such as x = 1, y = 7, z = 5 Now, check options (ii) & (iii) statement are correct.

Let x,y,z be positive integers such that HCF (x,y,z) = 1 and x2 + y2 = 2z2 . 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(x2 – y2)(A) I and II only(B) II and III only(C) II only(D) III only

Answer»

Correct option (B) II and III only

Explanation:

Take combination such as x = 1, y = 7, z = 5

Now, check options

(ii) & (iii) statement are correct.

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Let x,y,z be positive integers such that HCF (x,y,z) = 1 and x2 + y2 = 2z2 . 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(x2 – y2)(A) I and II only(B) II and III only(C) II only(D) III only

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