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

`A^2+B^2+C^2+D^2` In Ambalal Cuboid Theory-2,2

If `A=B=a` where a is any member of `[N,Z,Q,R]`

Put `A=a` given

`B=a` given

Then `C=a/2` means `C=A/2`

& `D=(3a)/2` means `D= 3/2 A`


Results: `A^2+B^2+C^2=D^2` becomes true for any

value of `a` where `a` is any member of `[N,Z,Q,R]`


Proof: `D^2-C^2=(3/2A)^2-(A/2)^2`

`=9/4 A^2-1/4 A^2`

`=2 A^2`

`=A^2+A^2`

`=A^2+B^2` ∴ `B = A` given

`∴ A^2+B^2+C^2=D^2`

Example 1:

`A=a, B=a, C=a/2, D=(3a)/2`

But `a=8` In `A^2+B^2+C^2=D^2`

Then `(8)^2+(8)^2+(4)^2=(12)^2`

`∴ 64+64+16=144`

Example 2:

Put `a=-12`

`(-12)^2+(-12)^2+(-6)^2=(-18)^2`

`∴ 144+144+36=324`

Example 3:

Put `a=(2.1)`

`(2.1)^2+(2.1)^2+(1.05)^2=(3.15)^2`

`4.41+4.41+1.1025=9.9225` >

Example 4:

Put `a=3 2/7` means `23/7`


`∴ (23/7)^2+(23/7)^2+(23/14)^2=(69/14)^2`

`∴ (46/14)^2+(46/14)^2+(23/14)^2=(69/14)^2`

`∴ 2116/196+2116/196+529/196=4761/196`



Now for your satisfaction, take `A=` any value `a

B=a, C=a/2, D=39/2`


And put in formula `A^2+B^2+C^2=D^2` to get

successful result.

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

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