the L.C.M of two number is 495 while their HCF is 5 . if their sum is 100 then what will be their difference
Answers
Answer:
Step-by-step explanation:
Let the two numbers be a and b respectively
As per the given data,
LCM = 495
HCF =5
As per a calculation in mathematics,
The product of HCF and LCM calculated for two numbers is equal to the product of two numbers themselves
LCM * HCF = a * b
Thus,
495 * 5 = ab
2475 = ab …1
Now, it is stated that,
a + b = 10
Thus, b = 10 - a… 2
Put 2 in 1, we have,
2475 = a(10 - a)
Which gives us,
2475 = - a^2 + 10a
On rearranging, we get,
a^2 - 10a + 2475 = 0
Using the formula method
B^2 - 4AC
Here B=-10, A=1 C=2475
(-10)^2 - 4(1)(2475)
= 100 - 4(2475)
= - 9800…which is less than 0
Thus, there exists no factors for equation
a^2 - 10a + 2475 = 0
Which implies no value of ‘a’ exists which satisfies the mentioned quadratic equation
As per 2, b depends on a, and hence as a does not exist, b also does not exist.
Conclusion : There does not exist any two numbers for which LCM is 495, HCF is 5 and their sum is 10.