Find the common theme with all these numbers. ( Except for the fact that all of them are wrong )

242 + 32 = 450

252 + 567 = 1575

507 + 147 = 1200

1805 + 20 = 2205

570312 + 19208 = 798848

(In reply to

answer by K Sengupta)

At the outset, we divide both sides of the first row by gcd of all

the three numbers in that row.

Now, in the first row, the three numbers are 242, 32 and 450, and gcd (242,32,450) = 2.

Then, the first row is now transformed to:

121 + 16 = 225

OR, 11^2 + 4^2 = 15^2

The above identity is obviously erroneous, but we note that inserting a square root ("v") symbol to each of the three numbers, we get the identity : 11 + 4 = 15, which is indeed true.

We are now in a position to conjecture that all the numbers in each of the five rows are missing the "v" symbol.

Accordingly, the requisite verification pertaining to all the the

five rows is furnished hereunder as follows:

*First Row:*

lhs = V242 + v32 = 11V2 + 4V2 = 15V2 = V450 = rhs

*Second Row*:

lhs = V252 + v567 = 6V7 + 9V7 = 15V7 = V1575 = rhs

*Third Row*:

lhs = V507 + v147 = 13V3 + 7V3 = 20V3 = V1200 = rhs

*Fourth Row*:

lhs = V1805 + v20 = 19V5 + 2V5 = 21V5 = V2205 = rhs

*Fifth Row*:

lhs = V570312 + v19208 = 534V2 + 98V2 = 632V2 = V798848 = rhs

Consequently, all the numbers in each of the five rows are

indeed missing the square root symbol.

*Note*:

Of course, the present exercise assumes that the "V" symbol

would yield only positive values. If the V symbol generated

positive values for some, but negative values for others, the

identity may not be valid.

Foer example, in the first row if V242 = 11V2 and V450 = 15V2,

but V32 = -4V2.

Then, lhs = (11 - 4)V2 = 7V2, which is not equal to rhs which is

15V2.