The product of the LCM and HCF of two natural numbers is 24 . The difference of two numbers is 2 . Find the numbers..
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Answered by
4
Let one number =x
Second number = x+2
Hence x*(x+2)=24
Or x^2+2x-24=0
I.e. (x+6)(x-4)=0
Now either x+6=0 i.e. x=-6
or x-4=0 i.e. x=4
Since the numbers are positive
Hence one numbers=x
And the second number=x+2=4+2= 6
4. and 4+2i.e. 6
4 and 6
Answered by
0
Step-by-step explanation:
As we know,
LCM x HCF = a * b ( a & b are numbers)
=> ab = 24
& (a- b ) = 2 ………( given)
Since, ( a+ b)² = (a -b)² + 4ab… ( identity)
=> (a+ b)² = 2² + 4 *24
=> (a+ b)² = 4 + 96 = 100
=> a+ b = 10 or -10 ……… (1)
But a - b = 2 …………..(2)
By solving above 2 equations by taking a+ b= +10
We get, 2a = 12
=> a= 6
=> b = 4
But if we take a+ b = -10
We get a = - 6 , b = -4 But for LCM & HCF, negative values can be discarded..
So, the numbers are 6 & 4
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