Published on 29th March 2018, City: Ahmedabad, Country : India.

Amblal 4D Theory 1 `A^2+B^2+C^2+D^2=E^2`

Take `a=1` where a is any member of `{N,Z,Q,R}`

`B=C=a`

`D=a^2`

`E=a^2+1`

Amblal 4D Theory: `(1^2)+(a^2)+(a^2)+(a^2)^2`

`=(a^2+1)^2`

Proof: `(1)^2+(a)^2+(a)^2+(a^2)^2`

`= 1^2+a^2+a^2+a^4`

`= 1+2a^2+a^4`

`=(1+a^2)^2`

So `(1)^2+(a)^2+(a)^2+(a^2)^2`

`=(a^2+1)^2`

So `A^2+B^2+C^2+D^2=E^2` is true

Example 1: Take `a=5`

`(1)^2+(5)^2+(5)^2+(25)^2=(26)^2`

`1+25+25+625=676` is true.

Example 2: Take `a=(-7)`

Then `(1)^2+(a)^2+(a)^2+(a^2)^2`

`=(a^2+1)^2`

become `1^2+(-7)^2+(-7)^2+((-7)^2)^2`

`=((-7)^2+1)^2`

`1+49+49+2401=2500` is True

Example 3: Take `a=2.9`

Then `(1)^2+(a)^2+(a)^2+(a^2)^2`

`=(a^2+1)^2`

become `(1)^2+(2.9)^2+(2.9)^2+[(2.9)^2]^2`

`=[(2.9)^2+1]^2`

`1+8.41+8.41+70.7281=(9.41)^2`

`1+8.41+8.41+70.7281=88.5481` is true

Example 4:

Take `a=2/3`

Then `(1)^2+(a)^2+(a)^2+(a^2)^2`

`=(a^2+1)^2`


`(1)^2+(2/3)^2+(2/3)^2+(4/9)^2`

`=((4/9) +1)^2=(13/9)^2`

`1(81/81)+(4(9))/(9(9))+(4(9))/(9(9))+16/81`

`=169/91`

`81+36+36+16=169` is true

means `A^2+B^2+C^2+D^2=E^2` is true

which denoted by `(1)^2+(a)^2+(a)^2+(a^2)^2`

`=(a^2+1)^2`

Your satisfaction take a = any value of `{N,Z,Q,R}` theory become True

For any doubt and additional details please contact me via Email : ambalalparmar40@yahoo.com

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