Question

Q11. If the sum of two natural numbers is 27 and their product is 182. Find the numbers. ​

Answer 1

see attached file for your answer

X = 13 or 14

Y = 14 or 13

Answer 2

Answer

• The required numbers are 13 and 14.

Given

• The sum of two natural number = 27 and their product = 182.

To Do

• To find the numbers.

Step By Step Explanation

Assumption :

Let the numbers be x and y respectively.

Then, ↓

x + y = 27 be eq. 1 and xy = 182 be eq. 2.

Now, x = 27 - y.

By substituting the value :

Let's substitute the value of x in eq. 2.

$\longmapsto \sf xy = 182 \\ \\\longmapsto \sf (27 - y)y = 182 \\ \\\longmapsto \sf 27y - {y}^{2} = 182\\\\ \bold{By\:splitting\:the\:middle\:term} \downarrow\\ \\ \longmapsto \sf {y}^{2} - 27y + 182 = 0 \\ \\\longmapsto \sf {y}^{2} - 13y - 14y + 182 = 0 \\ \\\longmapsto \sf y(y - 13) - 14(y - 13) = 0 \\ \\\longmapsto \sf (y - 13)(y - 14) = 0 \\ \\ \bold{Now} \downarrow\\ \\ \longmapsto \sf y - 13 = 0 \implies { \underline{ \boxed{ \bold {\pink{y = 13}}}}} \: \: \: \: \: \bigstar\\ \\\longmapsto \sf y - 14 = 0 \implies \underline{\boxed{ \bold{ \green{ y = 14}}}} \: \: \: \: \: \bigstar$

Therefore, the required numbers are 13 and 14.

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