The sum of two numbers is 20. their product is 96, then their hcf is
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Let the numbers be x, y
Given, x + y = 20 ....(1)
xy = 96....(2)
= > y = 20-x
substitute y = 20 - x in (2)
= > x(20 - x) = 96 = > 20x−x2=9620x−x2=96
= > x2–20x+96=0x2–20x+96=0
=> x=12 or 8
If x = 12, y= 20 - 12 = 8
If x = 8, y=20-8 = 12
The required 2 nos are 8 12
GCD of 8,12=4
Given, x + y = 20 ....(1)
xy = 96....(2)
= > y = 20-x
substitute y = 20 - x in (2)
= > x(20 - x) = 96 = > 20x−x2=9620x−x2=96
= > x2–20x+96=0x2–20x+96=0
=> x=12 or 8
If x = 12, y= 20 - 12 = 8
If x = 8, y=20-8 = 12
The required 2 nos are 8 12
GCD of 8,12=4
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3
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