## Matt71 3 years ago A number is expressed as N=(x^2-169)+(x-13)^2 1. Factorise (x^2-169)+(x-13)^2 completely 2. Explain why N is an even number for any value of x 3. Hence, given that N=(83^2-169)+70^2, without evaluating for N, find the 2 factors of N which are between 10 and 100

1. myininaya

So have you expanded N first by doing (x-13)(x-13)?

2. myininaya

And then you will collect like terms for N and then you can factor it

3. myininaya

completely!

4. Matt71

2x(x-13) right? But for me the real problem is with the second and last number

5. myininaya

Where did the extra x come from?

6. myininaya

wait sorry

7. myininaya

There is something missing though

8. myininaya

\[x^2-169+(x-13)^2\] \[x^2-169+(x^2-2(13)x+169)\] Is this what you did?

9. myininaya

Gosh you are right Its late here

10. myininaya

Ok So you have 2x(x-13) And it has the factors 2, x, x-13 Since it has the factor 2 , then that means N is divisble by 2 which means that N is ____?

11. Matt71

Eveeen ohohhhhh, of course, dang can't believe I missed that

12. himanshu31

first two parts have been explained by @myininaya for the last part put x=83 in 2x(x+13) u get 2*83*96..this means two factors are 83 and 96

13. himanshu31

sorry the eq is 2x(x-13)..factors are 83 and 70

14. Matt71

Well, thanks to you guys, sorry I only got one medal to give