Find the smallest number in gp whose sum is 38 and product is 1728.

Question

This problem is on geometric progression

Answer 1

"Find the smallest number. . .?"

Do you mean "find the smallest 3 numbers" or "find the smallest 3 consecutive numbers" or "find the smallest 4 numbers" or what?"

 

If you meant "find the smallest 2 numbers," there appears to be no solution:

x + y = 38

xy = 1728

x = 1728/y

1728/y + y = 38

1728 + y^2 = 38y

y^2 - 38y + 1728 = 0

Quadratic formula:

y = (-b +- sqrt( b^2 - 4ac) ) / 2a

y = (38 +- sqrt(38^2 -4*1*1728) ) /2

y = (38 +- sqrt(1444 - 6912) ) / 2

y = (38 +- sqrt(-5468) ) / 2

Can't do the square root of a negative number, so there's no solution.