Question

sum of squares of two consecutive natural number is 244 find the numbers

Answer 1

Hey

Here is your answer,

Let two consecutive natural number will be x and x+1

x^2 + (x+1)^2 = 244
x^2 x^2 +1 + 2x = 244
2x^2 + 1 + 2x = 244
2x^2 + 2x -243=0

solve this equation to get the answer

Answer 2

The sum of squares of two “consecutive natural number” is 244, the numbers will be “12 and 10”.    

Given:  

Sum of squares of two consecutive natural number is 244.

Solution:  

Let us consider the first number as x, then the second number will be x + 2  

It is given that the sum of squares of two consecutive natural number is 244.

This can be written in equation as under:

$\Rightarrow(\mathrm{x})^{2}+(\mathrm{x}+2)^{2}=244$

$\Rightarrow \mathrm{x}^{2}+\mathrm{x}^{2}+4 \mathrm{x}+4=244$

$\Rightarrow 2 x^{2}+4 x=244-4$

$\Rightarrow 2 x^{2}+4 x=240$

$\Rightarrow 2 x^{2}+4 x-240=0$

$\Rightarrow 2\left(\mathrm{x}^{2}+2 \mathrm{x}-120\right)=0$

$\Rightarrow\left(\mathrm{x}^{2}+2 \mathrm{x}-120\right)=0$

$\Rightarrow \mathrm{x}^{2}+12 \mathrm{x}-10 \mathrm{x}-120$

$\Rightarrow \mathrm{x}(\mathrm{x}+12)-10(\mathrm{x}+12)=0$

$\Rightarrow(x-10)(x+12)=0$

$\Rightarrow x=10,-12$

Thus, non be x= 12 & x = 10.