Question

find the two numbers whose product is 45 and their sum is 14

Answer 1

Answer: 9 and 5

Step-by-step explanation:

9×5=45

9+5=14.

Answer 2

$let \: the \: required \: numbers \: be \: (x) \: and \: (14 - x)$

Then,

$= x(14 - x) = 45 \\ \\ = 14x - {x}^{2} = 45 \\ \\ = 14x - {x}^{2} - 45 = 0 \\ \\ = - {x}^{2} + 14x - 45 = 0 \\ \\ = - {x}^{2} + 9x + 5x - 45 = 0 \\ \\ = - x(x - 9) + 5(x - 9) = 0 \\ \\ = (x - 9)( - x + 5) = 0 \\ \\ \\ x = ( + 9) \: or \: ( + 5)$
Hence, The required numbers are (x) = 9 & (14 - x) = 5




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