the sum of two number is 407. the sum and difference of their LCM and HCF are 925 and 851 respectively the difference of two number is----
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Let two no be a & b
so, a + b= 407..........(given)
LCM + HCF = 925..............(1)
LCM - HCF = 851..............(2)
Add eq (1)&(2),
2LCM = 1776 ➡LCM = 888
So, HCF = 925 - 888 = 37
We know that,
HCF * LCM = a*b
37 * 888 = ab
or 32856 = (407-b) * b (a+b=407)
32856 = 407b - b²
or b²-407b+32856=0
b² - 296b - 111b + 32856 = 0
b (b-296) - 111(b-296)
(b-111) (b-296)
b= 111 or b=296
So these are the two nos
& their difference is (a-b)
(296-111) = 185.
Hope it will help you !!!
so, a + b= 407..........(given)
LCM + HCF = 925..............(1)
LCM - HCF = 851..............(2)
Add eq (1)&(2),
2LCM = 1776 ➡LCM = 888
So, HCF = 925 - 888 = 37
We know that,
HCF * LCM = a*b
37 * 888 = ab
or 32856 = (407-b) * b (a+b=407)
32856 = 407b - b²
or b²-407b+32856=0
b² - 296b - 111b + 32856 = 0
b (b-296) - 111(b-296)
(b-111) (b-296)
b= 111 or b=296
So these are the two nos
& their difference is (a-b)
(296-111) = 185.
Hope it will help you !!!
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