Question

What is the sum of two consecutive numbers the difference of whose squares is 19?

Answer 1

Let the numbers be x and x+1
we knw that x²=(x+1)²-19
x²+19=x²+2x+1          {applying (a+b)²=a²+b²+2ab}
x²-x²+19-1=2x
18=2x
x=18/2=9
∴x=9,x+1=10
∴sum=9+10=19

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Answer 2

The numbers are 9 and 10.

GIVEN

Difference of squares of two consecutive numbers = 19

TO FIND

Sum of the numbers

SOLUTION

We can simply solve the above problem as follows;

We know consecutive numbers are those numbers that come one after the other.

Therefore,

Let the first number be x

Second number = x+1

It is given;

x² - (x+ 1)² = 19

x² = (x + 1)² - 19

Applying (a+b)² = a² + b² + 2ab

x² = (x² + 1 + 2x) - 19

Adding the like terms

x² - x² = 1 -19 + 2x

-18 + 2x = 0

2x = 18

x = 18/2 = 9

First number = x = 9

Second number = x+1 = 9+1 = 10

Hence, The numbers are 9 and 10.

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