Question

The sum of two consecutive natural numbers and the square of the first is 5329. What are the numbers?

Answer 1

Hint – In order to solve this problem we need to assume a variable as a natural number and make the conditions according to the problem and solve that equation to get the numbers.

Complete step-by-step solution -
Let the natural number be x then the number consecutive to x will be x + 1.
It is said that the sum of two consecutive natural numbers and the square of the first is 5329.
So, according to the above equation can be formulated as:
${\text{x + (x + 1) + }}{{\text{x}}^{\text{2}}}{\text{ = 5329}}$
On solving further we get,
${{\text{x}}^{\text{2}}}{\text{ + 2x + 1 = 5329}}$……………..(1)
We can say ${{\text{x}}^{\text{2}}}{\text{ + 2x + 1}}$ is nothing but ${{\text{(x + 1)}}^{\text{2}}}$
So, (1) can be written as:
${{\text{(x + 1)}}^{\text{2}}}{\text{ = 5329}}$
Then, ${\text{(x + 1) = }}\sqrt {5329} $
Square root of 5329 is nothing but 73.
So, x + 1 = 73
And x = 72
Therefore the two numbers are 72 and 73.
Note – To solve such questions we need to make equations according to the problem and solve to get the value of variables present in the equations. Try to assume a lesser number of variables this will make your problem easier and always remember that the number of equations with unknown variables must be equal to the number of unknown variables. Proceeding like this you will get the right answer.