Question

The sum of the square of two consecutive natural number is 313 find the number

Answer 1

Step-by-step explanation:

Let the two consecutive natural numbers be x and (x + 1). Hence,

${x}^{2} + (x + 1)^{2} = 313 \\ {x}^{2} + {x}^{2} + 2x + 1 - 313 = 0 \\ 2 {x}^{2} + 2x - 312 = 0 \\ {x}^{2} + x - 156 = 0 \\ {x}^{2} + 13x - 12x - 156 = 0 \\ x(x + 13) - 12(x + 13) = 0 \\ (x + 13)(x - 12) = 0 \\ x + 13 = 0 \: or \: x - 12 = 0 \\ x = - 13 \: or \: x \: = 12 \\ but \: x \in \: N \implies \: x \neq - 13 \: \\ \therefore x = 12 \\ \: \therefore x+1 = 12+1= 13$

Thus, the two consecutive natural numbers are 12 and 13.

Answer 2

Answer:

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