Question

find two numbers whose sum is 27 and product is 182

Answer 1

Hi friend,

Here is your answer,
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Let the numbers be x and y.
x+y = 27                                -----------------(i)
xy = 182                                -----------------(ii)

From (i) ,
x = 27- y

Put it in (ii)
(27- y)y = 182
27y - y² = 182
y²- 27y +182 = 0
y² - 14y - 13y + 182 = 0
y(y-14)+13(y-14) = 0
(y -13)(y - 14) = 0 
y -13 = 0          y - 14 = 0
     y  = 13              y  = 14

Required numbers are :- 13 and 14
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Answer 2

Hello..

x+y = 27

xy=182

x= 182/y

182/y+y =27

182+y^2=27

y^2-27y+182=0

y^2-14y-13y+182=0

y(y-14)*-13(y-14)=0

(y-14)(y-13)=0

y=14,y=13

when y=14,

x+14=27

⇒x=13

13 and 14