Question

If sum of two numbers is 55 and hcf and lcm are 5 and 120 then sum of reciprocal of number is

Answer 1

a²+b²=(a+b)² - 2ab

⇒a²+ b² =55²- 2 x 600

⇒ a² +b² =3025-1200

∴ a² + b² =1825

again,

a² +b² = ( a-b )² + 2ab

⇒ 1825 = ( a - b ) ² + 1200

⇒a - b =√1825-1200

∴ a- b =25

now adding both equation either side ,

a + b + a - b = 55+ 25

2a = 80

∴ a = 40

and b = 15

∴sum of its reciprocial

=1/40+ 1/ 15 =11/120