*** TOUGH Math Puzzler ***

Re: *** TOUGH Math Puzzler ***

Given:
N1 - N2 = 10
N1(N2) = 16

Solving:
From the first equation, N2 = N1 - 10
N1(N2) = N1(N1 - 10) = 16
Carrying out the multiplication, N1^2 -10N1 - 16 = 0

N1=

10 +/- SQRT(100 +64)
---------------------------
2

=

10 +/- 12.806
----------------
2

= 11.403, -1.403

N2 = N1 - 10 = 1.403, -11.403

So, both the pairs 11.403, 1.403 and -1.403, -11.403 are solutions, but, after inspection, I will regard them as the same solution.

Thus, we have N1 = 11.403, N2 = 1.403.
Now, to answer the question asked:

N1^2 = 130.

N2^2 = 1.97.

The sum of their squares is 131.97.

It's 132 (exactly).
Don't use approximations. Carry the radicals through to the end.

Okay:

N1 =

10 +/- SQRT(164)
---------------------
2

= 5 +/- SQRT(41) but use positive root so = 5 + SQRT(41)

N2 = N1 - 10 = -5 + SQRT(41)

N1^2 = 25 + 10 SQRT(41) + 41
N2^2 = 25 - 10 SQRT(41) + 41

N1^2 + N2^2 = 25 + 25 + 41 + 41 = 132

132

42

I think -32 is also a possibility (along with 132), since x could be 5 - (root)41, and y could be -5 - (root)41. The product of these 2 numbers is also 16.

But the sum of the squares is still 132.

Its Easy Dude ! :-)
Okay, I just had a look at all the answers. The problem isn't difficult and can be solved without having to use pen and paper. Let's see how.
We have:-
(a-b) = 10 &
ab = 16.
Now, remember (a-b)^2 = a^2 + 2ab + b^2.
Now (a-b)^2 + 2ab = (a^2 + b^2)
Therefore all we've to do is-
(10)^2 + 2 x 16 ... ( got it ? )
Therefore, answer is 100+32 = 132.
Simple !