Question

the product of two numbers is 45 and their sum is 14. find the numbers. {hint= (x-y) whole square = (x+y) whole square - 4xy}​

Answer 1

Answer:

9 and 5

Step-by-step explanation:

Let the numbers be x and y

given

$x + y = 14$

it implies that

$x = 14 - y \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (1)$

Also given that

$x \times y = 45$

substituting (1) in the above equation we have,

$(14 - y) \times y = 45$

$14y - {y}^{2} = 45$

${y}^{2} - 14y + 45 = 0$

factorizing we have

$(y - 9) \times (y - 5) = 0$

solving we have,

$y = 9 \: and \: y = 5$