Question

Sum of square of two consecutive natural no is 164

Answer 1

Hey mate here is your answer,
Let The Number be x and x + 2 ----[ Since The Numbers Are Even 
                                                             Numbers]

According To The Question,

x² + (x + 2)² = 164
x² + x² + 4x + 4 = 164
2x²  + 4x = 164 - 4
2x² + 4x -160 = 0

Dividing Whole Equation by 2
x² + 2x - 80 = 0
x² + 10x - 8x - 80 = 0
x(x + 10) -8(x + 10) = 0
(x - 8)(x + 10) = 0
x = 8 and not - 10 because x is a natural number
 
Therefore,

Answer = The Numbers Are 8and x + 2 = 8 + 2 = 10 
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Answer 2

Answer : 8 and 10

Solution :
_________

Given that : sum of square of two consecutive numbers is 164

Let, two consecutive numbers are x and (x+2)

Now, according to the question :

${x}^{2} + {(x + 2)}^{2} = 164 \\ \\ = > {x}^{2} + {x}^{2} + 4x + 4 = 164 \\ \\ = > 2 {x}^{2} + 4x - 160 = 0 \\ \\ = > {x}^{2} + 2x - 80 = 0 \\ \\ = > {x}^{2} + 10x - 8x - 80 = 0 \\ \\ = > x(x + 10) - 8(x + 10) = 0 \\ \\ = > (x + 10)(x - 8) = 0$

Required value of x = –10 and 8

The value of x = –10 doesn't exist.

So, the value of x = 8

And x+2 = 8+2 = 10

Thus, the two consecutive natural numbers will be 8 and 10