Question

The sum of the squares
of two consequtive natural
Number Is 3 13.find the number​

Answer 1

X 2 + ( X + 1 )2 = 313
X2 + X2 + 2X + 1 = 313
2X2 + 2X -312 = 0
X2 + X - 156 = 0
X2 + 13X -12X -156 = 0
X ( X + 13 ) -12 ( X + 13 ) = 0
X = 12 Or -13

Since it’s natural number, X = 12
Numbers are 12 & 13

Answer 2

Let the two consecutive natural numbers be x,x+1

==>x²+(x+1)²=313

==>x²+x²+2x+1=313

==>2(x²+x)=312

==>x²+x=156

==>x²+x-156=0

==>x²+13x-12x-156=0

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

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

==>x=12 (As the natural number cannot be negative,x is not equal to 13)

Therefore,x=12

x+1=12+1=13

So,The numbers are 12,13.

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