Question

The LCM of two numbers is 495 and their HCF is 5 .If the sum of these numbers is 10 difference is

Answer 1

Hey frnd...



Thanks for asking this question.
Here is your answer...

The solution is in the attachment.


Hope this would help you.

Answer 2

Heya !!!!

Ur question seems wrong, the difference should be 10.
So, I am answring according to me.


This is your answer.......

Given :-----

HCF = 5, and
LCM = 495.

Let the numbers be x and y.

We know that LCM × HCF = Product of the Numbers.

So, 495 × 5 = x × y
2475 = xy. .......(i).

Also, it is given that the difference (as the question is wrong) is 10.
So,

x - y = 10.
x = 10 + y .......(ii).

From equation (i) and (ii), we get........

(10+y)y = 2475
y² + 10y - 2475 = 0.

Factoring this polynomial.....

Looking at Prime factors of 2475 ...
2475 = 3 × 3 × 5 × 5 × 11

We get two numbers a and b such that a +b = 10 and ab= -2475.

Hence, the two numbers are 55 and -45.

So,
y² + 10y - 2475 = 0
y² +55y - 45y - 2475 = 0
y (y + 55) - 45 (y + 55) = 0
(y -45)(y+55) = 0

y = 45 and y = -55.

But, the number must be a whole number, So...

Y = 45.

Also, from equation (ii), we get

x = 10 + y
x = 10 + 45
x = 55.

Hence, the two numbers are 45 and 55.

Their sum = 45 + 55 = 100.

Hope you got the answer.....