If ab = 9 and a² + b² = 81, then (a+b)² = ?​

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If ab = 9 and a² + b² = 81, then (a+b)² = ?​

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Bình An 3 years 2021-08-22T05:26:12+00:00 1 Answers 3 views 0

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  1. Ben
    0
    2021-08-22T05:27:20+00:00
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    Answer:

    99

    Step-by-step explanation:

    Through some clever algebra, we can combine our first two equations using the fact that

    (a+b)^2=a^2+2ab+b^2

    We have the a² and the b² in the equation a^2+b^2=81, and we almost have a 2ab in the equation ab=9. To get that 2ab, we can simply double both sides of the first equation to get 2ab=18. From there, we’ll add the first two equations together, giving us the summed equation

    a^2+b^2+2ab=81+18\\a^2+2ab+b^2=99

    And since (a+b)^2=a^2+2ab+b^2, we can equivalently say that

    (a+b)^2=99

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