If (10 + ₁₀ x) , (10 + ₁₀ y) and (10 + ₁₀ z) are in AP, then consider the following statements: I. The GM of x and z is y^2 . II. The AM of ₁₀ x and ₁₀ z is ₁₀ y . Which of the statements given above is/are correct?

Step-by-step solution

Given (10 + ₁₀ x) , (10 + ₁₀ y) , and (10 + ₁₀ z) are in AP. 2(10 + ₁₀ y) = (10 + ₁₀ x) + (10 + ₁₀ z) 20 + 2 ₁₀ y = 20 + ₁₀ x + ₁₀ z 2 ₁₀ y = ₁₀ x + ₁₀ z ₁₀ y = ₁₀ x + ₁₀ z 2 This shows that the AM of ₁₀ x and ₁₀ z is ₁₀ y . Thus, Statement II is correct. From 2 ₁₀ y = ₁₀ x + ₁₀ z , we get: ₁₀ y^2 = ₁₀ (xz) y^2 = xz The GM of x and z is xz = y^2 = y . Thus, Statement I is incorrect. Only Statement II is correct. Answer: II only