LCM of two numbers is 105 ,HCF of that two numbers is 1,sum of the numbers is 22, the difference is ?
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Answered by
53
Let the numbers be a and b
a + b = 22
=> a = 22 - b ------(1)
Product of numbers = LCM × HCF
=> ab = 105 × 1
=> ( 22 - b) (b) = 105
=> 22b - b^2 = 105
=> 0 = 105 - 22b + b^2
=> b^2 - 22b + 105 = 0
=> b^2 - 15b - 7b + 105 = 0
=> b (b-15) - 7(b - 15) = 0
=> (b - 15) (b - 7) = 0
b = 15 and 7
When b = 15
a = 7
When b = 7
a = 15
Required difference = 15 - 7 = 8
a + b = 22
=> a = 22 - b ------(1)
Product of numbers = LCM × HCF
=> ab = 105 × 1
=> ( 22 - b) (b) = 105
=> 22b - b^2 = 105
=> 0 = 105 - 22b + b^2
=> b^2 - 22b + 105 = 0
=> b^2 - 15b - 7b + 105 = 0
=> b (b-15) - 7(b - 15) = 0
=> (b - 15) (b - 7) = 0
b = 15 and 7
When b = 15
a = 7
When b = 7
a = 15
Required difference = 15 - 7 = 8
ranju2005:
thnks
Answered by
3
Let the numbers be a and b
a + b = 22
=> a = 22 - b ------(1)
Product of numbers = LCM × HCF
=> ab = 105 × 1
=> ( 22 - b) (b) = 105
=> 22b - b^2 = 105
=> 0 = 105 - 22b + b^2
=> b^2 - 22b + 105 = 0
=> b^2 - 15b - 7b + 105 = 0
=> b (b-15) - 7(b - 15) = 0
=> (b - 15) (b - 7) = 0
b = 15 and 7
When b = 15
a = 7
When b = 7
a = 15
Required difference = 15 - 7 = 8
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