Question

LCM = 990 HcF = 10 sum of two numbers is 200 .... Find the difference! plz give me a solved answer i wil make you brainlist​

Answer 1

Answer:

The required numbers are: 110, 90

Step-by-step explanation:

Let the required numbers be 'a' and 'b'

By the given conditions,

a + b = 200

b = 200 - a -----------( 1 )

we know that,

product of two numbers = LCM x GCD

given, LCM = 990

GCD = 10

=> a x b = 990 x 10

ab = 9900

substituting ( 1 )

=> a ( 200 - a ) = 9900

200a - a^2 = 9900

a^2 - 200a + 9900 = 0

by solving the quadratic equation, we get,

( a - 90 ) ( a - 110 ) = 0

a = 90 (or) a = 110

when, a = 90,

90 + b = 200

b = 110

when, a = 110,

110 + b = 200

b = 90

therefore the required numbers are 110 and 90

I hope this is helpful :)