Question

What two numbers have a sum of 17 and a product of 66

Answer 1

let two numbers be x and y.

according to question:

x × y = 66 and x + y = 17

x= 66/y

put it in x+ y=17

66/y + y=17

66+ y^2 = 17y

y^2 -17 +66 = 0

y^2 -11y -6y + 66 = 0

y(y-11) - 6(y-11) = 0

(y-11) (y-6) = 0

therefore, y = 11 or 6

if y=11 : x= 6

if y=6 : x= 11

thus, the two numbers are 11 and 6.

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Answer 2

Answer:

11 and 6

Step-by-step explanation:

Let, two numbers are a and b .

1st conditions, a+b= 17 ---->i

2ns conditions, ab= 66

therefore, (a+b)^2 =17^2

or, (a-b) ^2+4ab = 289

or, (a-b)^2 + 4*66=289

or, (a-b)^2 = 289-264=25

or, (a-b)= 5 ---->ii

by addition of i and ii.

2a = 22

so, a = 22/2=11

therefore,one number is 11 and others is 66/11=6