Question

the sum of squares of 2 consecutive even natural number is 164 find the number

Answer 1

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

Let the first no. be x so the second would be x+2(as they are both even no.s)
$x^{2} + (x+2)^{2}$ =164
$x^{2} + x^{2}$ + 4+4x=164
2$x^{2}$+4x+4=164
$x^{2}$+2x+2=82
$x^{2}$+2x-80=0
D=$b^{2}$-4ac
  =$2^{2}$-4(1)(-80)
   =4+320
      =324
x=-b+/-$\sqrt{D}$/2a

x=-b+$\sqrt{D}$/2a
 =-2+√324/2(1)
  =-2+18/2=16/2=8

x=-b-$\sqrt{D}$/2a
 =-2-√324/2=-20/2=-10
But since it is given that hey are natural numbers -10 cannot be possible as it is a negative term

there fore x=8 and net no. is x+2=8+2=10

Therefore the numbers are 8 and 10

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