Question

the sum of two numbers is 16 and their product is 63

Answer 1

Answer:

The numbers are 7 and  9

Step-by-step explanation:

let the numbers be x and y.

now, x + y = 16 .................   (i)

and xy =  63 ......................  (ii)

now, y= 16 - x  ......................(iii)

substitute eq (iii) in eq (ii)

x(16 - x) = 63

16x - x² = 63

x² - 16x + 63 = 0

x² - 7x -9x + 63 = 0

x(x-7) -9(x-7)

(x-9)(x-7) = 0

x= 9 or x = 7

if x= 9,

then 9×y= 63

y=7

if x= 7

7×y= 63

y=7

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Answer 2

Let numbers are x and y

x+y=16........(1)

xy=63

x=63y.........(2)

Put the value of x in (1)

63/y+y=16

Multiply by y both sides

63+y^2=16y

Rearrage above equation

y^2-16y+63=0

y^2-9y-7y+63=0

y(y-9)-7(y-9)=0

(y-7)(y-9)=0

y-7=0 or y-9=o

y=7 or y=9

Put the values of y in (1)

x=7

x+y=16

x+7=16

x=16-7

x=9

x+9=16

x=16-9

x=7

if one number is 7 other will be 9 or one is 9 other will be 7.

So numbers are 7 and 9