Question

The difference between two numbers is 6, product is 16.find the numbers​

Answer 1

Let the numbers be x & y.

Then, by the first condition,

Average of x & y=

2

x+y

=6

⟹x+y=12 .......(i)

And by the second condition,

2(x−y)=16

⟹x−y=4 .......(ii)

(i)+(ii)⟶2x=16

⇒x=8

Substituting x=8 in (i),

⇒8+y=12

⇒y=4

So, the numbers are 8 & 4.

HOPE THIS HELPS YOU ❤️

Answer 2

$\huge\bold\colorbox{indigo}{Answer:}$

❥︎ Let the two numbers be x(larger) & y(smaller).

❥︎ The difference between the two numbers is 6.

➪ x - y = 6 .....(i)

❥︎ The product of the two numbers is 16.

➪ x * y = 16 .....(ii)

➪ x = 16/y .....(iii)

❥︎ Take the value of x from equation (iii) in equation(i):

➪ (16/y) - y = 6

➪ (16 - y²)/y = 6

➪ 16 - y² = 6y

➪ y² + 6y - 16 = 0

➪ y² + 8y - 2y - 16 = 0

➪ y(y + 8) - 2(y + 8) = 0

➪ (y - 2) (y + 8) = 0

➪ (y - 2) or (y + 8) = 0

➪ (y - 2) = 0 or (y + 8) = 0

➪ y = 2 or y = (-8)

❥︎ Taking value of y = 2 in equation (ii):

➪ x * 2 = 16

➪ x = 8

❥︎ Taking value of y = (-8) in equation (ii):

➪ x * (-8) = 16

➪ x = (-2)

❥︎ Therefore, the pair of numbers are 8 & 2 or (-2) & (-8).

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