Question

Find two numbers whose sum is 27 and product is 182.

Answer 1

Hi friend
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Your answer
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SOLVING (BY METHOD OF COMPARISON )
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Let the the numbers be x and y respectively.

Then,
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According to the question,
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Equations
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x + y = 27 .....(i)

xy = 182 ......(ii)

From equation (i), we get,

x = 27 - y.....(iii)

From equation (ii), we get,

x = 182/y.......(iv)

Now, on comparing the values of x from equations (iii) and (iv), we get,

27 - y = 182/y

=> y(27 - y) = 182

=> 27y - y² = 182

=> - y² + 27y - 182 = 0

=> - y² + 14y + 13y - 182 = 0

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

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

Now,
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y - 14 = 0

=> y = 14

Then, x = 182/y = 182/14 = 13

x = 13 and y = 14

OR

When,

13 - y = 0

=> y = 13

Then, x = 182/y = 182/13 = 14

x = 14 and y = 13

Therefore,
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The numbers are 13 and 14.

HOPE IT HELPS

Answer 2

♧♧HERE IS YOUR ANSWER♧♧

Let us consider that the numbers are a and b.

Then, by the given conditions,

a + b = 27 ....(i)

and

ab =182 .....(ii)

From (i), we get

a = 27 - b and putting this value in (ii), we get

(27 - b)b = 182
or, b² - 27b + 182 = 0
or, b² - 13b - 14b + 182 =0
or, b(b - 13) - 14(b - 13) = 0
or, (b - 13)(b - 14) = 0

So, either b - 13 = 0 or, b - 14 = 0

Hence, b = 13 and b = 14

When, b = 13, When b = 14,
a = 27 - 13 = 14 a = 27 - 14 = 13.

Thus, the two numbers are 14 and 13.

♧♧HOPE THIS HELPS YOU♧♧