Question

find two numbers whose sum is 27 and product is 182

Answer 1

Let the two no. be X and Y

Their sum is 27

x+y=27
x. = 27-y

Product of two no. is 182

x×y=182

(27-y)×(y)= 182

27y-y² = 182

y²-27y+182=0

y²-14y-13y+182=0

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

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

y-14=0
y=14(Accepting)

y-13=0
y. = 13(Neglecting)



Thus Y=14

and X=27-y

x= 27-14=13

Answer 2

Let the first number =x

Let the second number =y

Sum =27

ATP

x+y=27

x=27-y-----------(1)

Its product=182

ATP

x*y=182

putting the value of x

(27-y)*y=182

27y-y2=182=0

y2-27y+182=0

y2-(14+13)y+182=0

y2-14y-13y+182=0

y(y-14)-13(y-14)

(y-14)(y-13)

y=14,y=13

putting the value of x in (1)

x=27-y. ,x=27-y

x=27-14. x=27-13

x=13. x=14

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