Question

The sum of the squares of two consecutive natural numbers is 85.Find the numbers

Answer 1

Answer:

6,7

6^2=36

7^2=49

sum them up to get 85..

Method: Introspection Method.☺️

Answer 2

Questions

The sum of square of two successive nature number is 85, the find the number.

Solution

Let two successive number be x and x+1

According to question

${x}^{2} + ( {x + 1)}^{2} = 85$

${x}^{2} + {x}^{2} + 2x + 1 = 85$

$2 {x}^{2} + 2x = 84$

${x}^{2} + x - 45 = 0$

${x}^{2} + 7x - 6x - 42 = 0$

$x(x + 7) - 6(x + 7) = 0$

$(x + 7)(x - 6) = 0$

$x + 7 = 0 \: \: \: or \: \: x - 6 = 0$

$x = - 7 \: \: or \: \: x = 6$

-7 is not a natural number, therefore not accepted

Or x=6

Therefore, required nature number are 6 and 6+1=7