Question

the difference between two numbers is 9 and the product of the numbers is 162. find the number.

Answer 1

See one number is number is 9 then there then their product is 162 another number is 162 divided 9 is equal to 18 is an answer

Answer 2

Answer :


Let the two numbers be x and y


ATQ -

$\binom{x - y = 9}{xy = 162} \\ \\ solve \: for \: x \\ \\ \binom{x = 9 + y }{xy = 162} \\ \\ substitute \: the \: value \: of \: x \: in \: the \: equation \: xy = 162 \\ \\ (9 + y)y = 162 \\ \\ solve \: for \: y \\ \\ 9y + {y}^{2} = 162 \\ \\ 9y + {y}^{2} - 162 = 0 \\ \\ {y}^{2} + 9y - 162 = 0 \\ \\ solve \: the \: quadratic \: equation \:$

$we \: get \\ \\ y = \frac{ - 9 + \sqrt{ {9}^{2} - 4 \times 1 \times ( - 162} }{2 \times 1} \\ \\ y = \frac{ - 9 + \sqrt{81 + 648} }{2} \\ \\ y = \frac{ - 9 + \sqrt{729} }{2} \\ \\ y = \frac{ - 9 + 27}{2} \\ \\ y = \frac{18}{2} \\ \\ y = 9$

$substitute \: the \: value \: of \: y \: in \: equation \: x = 9 + y \\ \\ x = 9 + 9 \\ \\ x = 18$

Therefore two numbers are 9 and 18

Verification---

=> 18 - 9 = 9

=> 18 × 9 = 162

Therefore, 18 and 9 are the two who when subtracted equals 9 and when multiplied equals 162


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