Question

The difference of two number is 14 their lcm and hcf are 441 and 7 respectively find the numbers

Answer 1

x-y = 14

y = x-14

LCM(x,y) x HCF(x,y)= 441 x 7 = xy

3087 = x(x-14)

0 = x^2 - 14x- 3087

x^2 -63x +49x -3087=0

x(x-63)+49(x-63)=0

(x+49)(x-63)=0

x= -49 (not possible)

or 63

therefore x=63

y= x-14

y=63-14

  = 49

therefore the numbers are 63 and 49