## HOW TO FIND TWO NUMBERS THAT SUM AND PRODUCT IS GIVEN

How to Find Two Numbers that Sum and Product is Given ?

In the section, we will learn how to solve word problems involving numbers.

Example 1 :

The sum of two numbers is 60 and their product is 576. Find the numbers.

Solution :

Let x and y are the two consecutive integers

The sum of two numbers is 60

x + y  =  60  ---- (1)

Product of two numbers  =  576

xy  =  576

y  =  576/x  ----- (2)

Now we apply the value of x in (1)

x + (576/x)  =  60

(x2 + 576) / x  =  60

x2 + 576  =  60x

x2 - 60x + 576  =  0

(x - 12) (x - 48)  =  0

 x - 12  =  0x  =  12If x  =  12y  =  576 / 12y  =  48 x - 48  =  0x  =  48If x  =  48y  =  576 / 48y  =  12

So the required integers are 18 and 48.

Verification :

The sum of two numbers is 60

48 + 18  =  60

60  =  60

The product is 576

48 (18)  =  576

576  =  576

Example 2 :

Two positive numbers differ by 4 and their product is 192. Find the numbers.

Solution :

Let x and y be two positive numbers

It differs by 4

x - y  =  4

x  =  4 + y   --- (1)

Their product is 192

xy  =  192

y  =  192/x --- (2)

By applying the value of y in (1), we get

x  =  4 + (192/x)

x  =  (4x + 192)/x

x2  =  4x + 192

x2 - 4 x - 192  =  0

(x - 16) (x + 12)  =  0

 x - 16  =  0x  =  16 x + 12  =  0x  =  -12

If x  =  16

Then,

y  =  192/16

y  =  12

Since it is positive number we have to choose 16 for x.

Verification :

It differs by 4

16 - 12  =  4

4  =  4

Their product is 192

(16) (12)  =  192

192  =  192

After having gone through the stuff given above, we hope that the students would have understood how to solve word problems of f

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