Question

If the A.M. of two numbers is 34 and the G.M. of the same two numbers is 16, find the greater number.

Answer 1

Explanation:

A.M. = 34

(a + b)/2 = 34

a + b = 68 -----(1)

G.M. = 16

√ab = 16

ab = 256

4ab = 1024 -----(2)

equation (1) & (2) Se

(a+b)² - 4ab = (a-b)²

(68)² - 1024 = (a-b)²

4624 - 1024 = (a-b)²

(a-b)² = 3600

a - b = 60 -----(3)

equation (1) + (3) Se

2a = 128

a = 64

equation (1) Se

64 + b = 68

b = 4

The greater number is a = 64

Answer 2

Explanation:

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