Matematika

Pertanyaan

hitunglah nilai dari (√5+√6+√7)(√5+√6-√7)(√5-√6+√7)(-√5+√6+√7) adalah

1 Jawaban

  • misal :
    a = √5 , aa = 5 , aaaa = 25
    b = √6 , bb = 6 , bbbb = 36
    c = √7,  cc= 7,  cccc = 49

    (a + b + c) (a + b - c)
    a(a + b - c) = aa + ab - ac
    b(a + b - c) = ab + bb - bc
    c(a + b - c) = ac + bc - cc
    (a + b + c)(a + b - c) = aa + bb - cc + 2ab

    (a - b + c)(-a + b + c)
    a (-a + b + c) = -aa + ab + ac
    -b(-a + b + c) = ab - bb - bc
    c(-a + b + c) = -ac + bc + cc
    (a - b + c) (- a + b + c) = -aa - bb + cc + 2ab

    ( aa + bb - cc + 2ab) (-aa - bb + cc + 2ab)
    aa(-aa - bb + cc + 2ab) = -aaaa - aabb + aacc + 2aaab
    bb (-aa - bb + cc + 2ab) = -aabb - bbbb + bbcc + 2abbb
    -cc( -aa - bb + cc + 2ab) = aacc + bbcc - ccccc - 2abcc
    2ab (-aa - bb + cc + 2ab) = -2aab - 2abbb + 2abcc + 4aabb

    ( aa + bb - cc + 2ab) (-aa - bb + cc + 2ab)
    = -aaaa - bbbb - cccc - 2aabb + 2aacc + 2bbcc + 4aabb
    = - 25 - 36 - 49 - 2. 5.6 + 2. 5. 7 + 2 . 7. 6 + 4. 5 .6  
    = - 100 - 60 + 70 + 84  + 120
    = 104


    maaf kalo salah

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