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Matt71

  • 2 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

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  1. myininaya
    • 2 years ago
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    So have you expanded N first by doing (x-13)(x-13)?

  2. myininaya
    • 2 years ago
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    And then you will collect like terms for N and then you can factor it

  3. myininaya
    • 2 years ago
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    completely!

  4. Matt71
    • 2 years ago
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    2x(x-13) right? But for me the real problem is with the second and last number

  5. myininaya
    • 2 years ago
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    Where did the extra x come from?

  6. myininaya
    • 2 years ago
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    wait sorry

  7. myininaya
    • 2 years ago
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    There is something missing though

  8. myininaya
    • 2 years ago
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    \[x^2-169+(x-13)^2\] \[x^2-169+(x^2-2(13)x+169)\] Is this what you did?

  9. myininaya
    • 2 years ago
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    Gosh you are right Its late here

  10. myininaya
    • 2 years ago
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    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
    • 2 years ago
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    Eveeen ohohhhhh, of course, dang can't believe I missed that

  12. himanshu31
    • 2 years ago
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    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
    • 2 years ago
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    sorry the eq is 2x(x-13)..factors are 83 and 70

  14. Matt71
    • 2 years ago
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    Well, thanks to you guys, sorry I only got one medal to give

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