*** TOUGH Math Puzzler ***

13-3=10
13+3=16

13x13=169
3x3=9

169+9=178

(is using a calculator cheating?)

I dont think this is right - help me:-)
13-3=10 Difference
13+3=16 <-- This cannot be the Product, a Product is derived by multiplication - correct?

(13x13) = 169
(3x3) = 9

169+9 = 178

i knew it couldn't be that easy

132

shall I do the full calculation?

x + y = 10
xy = 16

y = 10 - x

x (10 - x) = 16
10x - x^2 = 16
x^2 - 10x + 16 = 0

(x-2)(x-8) = 0
x = 2 then y = 8 or x = 8 then y = 2

2^2 + 8^2 = 4 + 64 = 68

The two numbers are:

11.4031242374328487
1.4031242374328487


Whim

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.

Your lack of precision has led you to the wrong answer.

N1 = 5 +/- sqrt(41)
N2 = -5 +/- sqrt(41)

Using the solution where both are positive:

N1^2 = 25 + 10sqrt(41) + 41 = 66 + 10sqrt(41)
N2^2 = 25 - 10sqrt(41) + 41 = 66 - 10sqrt(41)

N1^2 + N2^2 = 132 (exactly)

duh, I didn't read... I thought it said the SUM was 10... I figured it was so easy...

So, I'll just agree with all of you... :p

Another riddle:

This problem was also posted in the Math forum.
Brandon9000: Tue Mar 08, 2005 9:31 am Post: 1211036. (Note time) replied.

The original poster:
Gmoses: Tue Mar 08, 2005 12:38 pm Post: 1211388. (Note time) replied here with the answer given by Brandon 9000.

Confused? Well, I am. Is Gmoses, Brandon9000?


Markr is of cause, correct in his answer.