hitunglah nilai dari (√5+√6+√7)(√5+√6-√7)(√5-√6+√7)(-√5+√6+√7) adalah
Matematika
mufidsadzil
Pertanyaan
hitunglah nilai dari (√5+√6+√7)(√5+√6-√7)(√5-√6+√7)(-√5+√6+√7) adalah
1 Jawaban
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1. Jawaban Voslaarum
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