Question

Sum of the squares of 2 consequitve natural numbers is 313 find the number

Answer 1

Hey there !!


Let the two consecutive number be x and x + 1.

▶ Now,

A/Q,

=> x² + ( x + 1 )² = 313.

=> x² + x² + 2x + 1 = 313.

[ → ( a + b )² = a² + 2ab + b² . ]

=> 2x² + 2x = 313 - 1.

=> 2x² + 2x = 312.

=> 2x² + 2x - 312 = 0.

=> 2( x² + x - 156 ) = 0.

=> x² + x - 156 = $\frac{0}{2} .$

=> x² + x - 156 = 0.

=> x² + 13x - 12x - 156 = 0.

=> x( x + 13 ) - 12( x + 13 ) = 0.

=> ( x - 12 ) ( x + 13 ) = 0.

=> x - 12 = 0. | x + 13 = 0.

=> x = 12. | x = -13.

[ → Natural number is never in negative form ].

So, x = 12.

▶ Therefore, the numbers are 12 and 13.
[ x = 12 ; x + 1 = 12 + 1 = 13. ]


✔✔ Hence, it is solved ✅✅.

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THANKS

#BeBrainly.

Answer 2

We already know that consecutive natural numbers differ by one(1).

Hence,
If we assume the first number be ' x ' then the second number be ' x + 1 '.
Therefore,
The consecutive natural numbers will be ' x' and ' x + 1 ' .

If we read the question carefully we come to know that the sum of squares of these consecutive natural number is 313.

Therefore we can form the following equation and solve it,

( x ) ^ 2 + ( x + 1 ) ^ 2 = 313
or x^2 + x^2 + 2x + 1 = 313
or 2x^2 + 2x + 1 = 313
or 2x^2 + 2x - 312 = 0
or 2 ( x^2 + x - 156 ) = 0
or x^2 + x - 156 = 0

On splitting ' x ',

x^2 + 13x - 12x - 156 = 0
or x ( x + 13 ) - 12 ( x - 13 ) = 0
or ( x + 13 ) ( x - 12 ) = 0

Following the zero product rule, we will find two values for ' x ' .
( x + 13 ) = 0
x = - 13

OR

( x - 12 ) = 0
x = 12

Therefore, we get two values for ' x ',
x = 12 | x = - 13

Now since natural numbers are always positive,
We will consider the positive value of ' x '.

First number = x = 12
Second number = x + 1 = 12 + 1 = 13