What are some easy ways to find the value of (2017^4−2016^4)/(2017^2+2016^2) without calculator

Question

What are some easy ways to find the value of
(2017^4−2016^4)/(2017^2+2016^2) without calculator

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Thạch Thảo 5 years 2021-09-02T11:35:19+00:00 1 Answers 22 views 0

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  1. Sapo1
    0
    2021-09-02T11:37:01+00:00
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    Answer:

    4033

    Step-by-step explanation:

    An easy way to solve this problem is to notice the numerator, 2017^4-2016^4 resembles the special product a^2 – b^2. In this case, 2017^4 is a^2 and 2016^4 is b^2. We can set up equations to solve for a and b:

    a^2 = 2017^4

    a = 2017^2

    b^2 = 2016^4

    b = 2016^2

    Now, the special product a^2 – b^2 factors to (a + b)(a – b), so we can substitute that for the numerator:

    \frac{(2017^2+2016^2)(2017^2 - 2016^2)}{2017^2+2016^2}

    We can notice that both the numerator and denominator contain 2017^2 + 2016^2, so we can divide by \frac{2017^2+2016^2}{2017^2+2016^2} which is just one, and will simplify the fraction to just:

    2017^2 – 2016^2

    This again is just the special product a^2 – b^2, but in this case a is 2017 and b is 2016. Using this we can factor it:

    (2017 + 2016)(2017 – 2016)

    And, without using a calculator, this is easy to simplify:

    (4033)(1)

    4033

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )