Question

The sum of two numbers is 25. their product is 154

Answer 1

The two numbers are 14 and 11

Answer 2

Let those numbers be a and b

a+b = 25 -----(i)
ab = 154 -----(ii)

from (ii)
a = 154/b

by substituting for "a" in (i)

a + b = 25
(154/b) + b = 25
( 154 + b^2)/b = 25
154 + b^2 = 25b
154 + b^2 -25b =0

now, arrange the terms

b^2 - 25b + 154 = 0
b^2 - 14b - 11b + 154 =0
b (b-14) -11 (b-14) =0
(b-11)(b-14)= 0


now find the value for b

b -11 =0
b = 11
and

b-14=0
b = 14


b equals either 14 or 11

and a = 154/b
if b = 11 then, a = 154/11 = 14
if b = 14 then, a = 154/14 = 11


so, the value of a and b are 11 and 14.

so, those numbers are 11 and 14.