algebra

sum of two numbers is 80 and the sum of their reciprocal is 4/75. Find the two numbers.


Answer:
let the numbers be a and b.
given, a + b = 80
and 1/a + 1/b = 4/75
or, (a + b)/ab = 4/75
or, 80/ab = 4/75
or, 80/ab = 80/1500, multiplying Nr and Dr by 20.
comparing, LHS and RHS, we get
ab = 1500
therefore, Or, (a – b)² = (a + b)² – 4ab

Or, (a – b)² = (80)² – 4.1500

Or, (a – b)² = 6400 – 6000

Or, (a – b)² = 400

Or, (a – b) = 20

or, a = 50, b = 30