Question

The sum of the square of two consecutive natural numbers is 313. The numbers are ..... *

1)12,-13
2)13,14
3)11,12
4)14,15​

Answer 1

Answer:

1)12,-13

12*12+(-13*-13

144+169

=>313

Answer 2

Solution

Given :-

• The sum of the square of two consecutive natural numbers is 313.

Find :-

• These Number.

Explanation

Let, these number be x & x +1,

So, A/C to question,

==> x² + (x+1)² = 313

==> x² + x² + 1 + 2x = 313

==> 2x² + 2x - 312 = 0

==> x² + x - 156 = 0

==> x² + 13x - 12x - 156 = 0

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

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

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

==> x = 12 Or x = -13

Hence

case(1).

• when, x = 12

So,

• First number will be = 12
• Second Number will be = (12+1) = 13

Case(2).

• when , x = -13

So,

• First number will be = -13
• Second number will be = (-13+1) = -12

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