IF G.m between two number is 8 and their A.m is 10.find the numbers
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Answer:
Step-by-step explanation:
Let a and be be the two numbers
AM = a + b/2 = 10
=> a + b = 20 --------------- (1)
GM = √ab = 8
=> ab = 64.
=> a = 64/b --------------------(2)
Substitute (2) in (1)
64/b + b = 20
=> b² + 64 = 20b
=> b² - 20b + 64 = 0
=> b² - 16b - 4b + 64 = 0
=> b(b - 16) - 4(b - 16) = 0
=> (b - 4)(b-16) = 0
=> b = 4 or 16.
Substitute value of b in (2) to get a.
a = 64/b
if b = 4, a = 64/4 = 16.
if b = 16, a = 64/16 = 4.
Thus the numbers are 16,4 or 4,16.
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