Question

The diff of 2 numbers is 14 lcm is 441 hcf is 7

Answer 1

Answer is in the attachment.

Here, I've taken the numbers to be positive only.

Answer 2

• Let two numbers be M and N.

» The difference of two numbers is 14..

=> M - N = 14

=> M = 14 + N ______ (eq 1)

______________________________

• LCM = 441

• HCF = 7

» We know that

Product of two numbers = HCF × LCM

=> M × N = 7 × 441

=> MN = 3087

=> (14 + N)N = 3087

=> 14N + N² = 3087

=> N² - 14N - 3087 = 0

Now..

N = $\dfrac{ - b \: ± \sqrt{( {b)}^{2} \: - \: 4ac } }{2a}$

Here..

a = 1, b = - 14, c = - 3087

=> $\dfrac{ - ( - 14) \: ± \sqrt{( {14)}^{2} \: - \: 4 \: \times \: 1 \: \times \: ( - 3087)} }{2 \: \times \: 1}$

=> $\dfrac{ + 14 \: ± \sqrt{196 \: + \: 12348} }{2}$

=> $\dfrac{ + 14 \: ± \sqrt{12544} }{2}$

=> $\dfrac{14\:+\:112}{2}$

=> $\dfrac{126}{2}$

=> 63

• Similarly..

=> $\dfrac{14\:-\:112}{2}$

(Neglected because it's value came in negative).

• Put value of N in (eq 1)

=> M = 14 + 63

=> M = 77

_____________________________

The numbers are : 77 and 63

__________ [$\bold{ANSWER}]$