Question

Find two numbers whose sum is 27 and product is 182

Answer 1

HELLO USER ✌

HERE'S YOUR ANSWER FRIEND,

LET THE TWO NUMBERS BE X AND Y

THUS,

ACCORDING TO THE QUESTION

FIRST CASE :

==> X + Y = 27 ...........................(1)

AND,

SECOND CASE :

==> XY = 182 ..............................(2)

FROM (1) WE HAVE,

Y = 27 - X ...................................(3)


NOW, ON SUBSTITUTING (3) IN (2)

WE HAVE,

XY = 182

==> X(27 - X) = 182

==> 27X - X² = 182

ON CHANGING THE SIGNS WE HAVE,

==> X² - 27X + 182 = 0

==> X² - 14X - 13X + 182 = 0

==> X(X - 14) - 13(X - 14) = 0

==> (X - 14) + (X - 13) = 0

==> X = 14 AND X = 13

ARE THE REQUIRED TWO NUMBERS.

HOPE IT HELPS YOU.

$<marquee>$ #FROM KENDRIYA VIDYALAYA GANESH KHIND PUNE ✌

Answer 2

Answer :

Given that The sum of Two numbers is 27 and Product is 182

So, Let the Two Numbers be x and y

Then, ATQ ---

=> x + y = 27

=> x × y = 182

$= > \: \binom{x + y = 27}{x \times y = 182} \\ \\ = > \: firstly \: solve \: the \: equation \: for \: x \: \\ \\ = > \: x + y - y = 27 - y \\ \\ = > \: x = 27 - y \\ \\ = > \: we \: get \: - - \\ \\ = > \: \binom{x = 27 - y}{xy = 182} \\ \\ = > \: now \: substitute \: the \: value \: of \: x \: in \: the \: equation \: xy \: = \: 182 \\ \\ = > \: (27 - y)y = 182$

$= > \: solve \: the \: equation \: for \: y \\ \\ = > \: 27y - {y}^{2} = 182 \\ \\ = > \: 27y - {y}^{2} - 182 = 0 \\ \\ = > \: - {y }^{2} + 27y - 182 = 0 \\ \\ = > \: {y}^{2} - 27y + 182 = 0 \\ \\ = > \: y = \frac{ \sqrt{ - ( - 27) {}^{2} - 4 \times 1 \times 182 } }{2 \times 1}$

$= > \: y = \frac{27 + \sqrt{729 - 728} }{2} \\ \\ = > \: y = \frac{27 + \sqrt{1} }{2} \\ \\ = > \: y = \frac{27 + 1}{2} \\ \\ = > \: y = \frac{28}{2} \\ \\ = > \: y = 14 \\ \\ = > \: subsitute \: the \: value \: of \: y \: in \: the \: equation \: x = 27 - y$

$= > \: x = 27 - 14 \\ \\ = > \: x = 13 \\ \\ = > \: therefore \: x \: = 13 \: and \: y \: = 14 \\ \\ \\ = > \: verification \: \\ \\ = > \: 13 + 14 = 27 \\ \\ = > \: 13 \times 14 = 182$

Hence, Two numbers are 13 and 14

Hope it would help you