Jika diketahui |a|=4, |b|=2, dan a×(a-b)= 12, maka nilai |a+b| sama dengan?
Matematika
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Pertanyaan
Jika diketahui |a|=4, |b|=2, dan a×(a-b)= 12, maka nilai |a+b| sama dengan?
1 Jawaban
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1. Jawaban arsetpopeye
|a| = 4, |b| = 2
a.(a - b) = 12
a.a - a.b = 12
|a|^2 - a.b = 12
4^2 - a.b = 12
16 - a.b = 12
-a.b = -4
a.b = 4
|a + b|^2 = a.a + 2a.b + b.b
|a + b|^2 = |a|^2 + 2 a.b + |b|^2
|a + b|^2 = 4^2 + 2 (4) + 2^2
|a + b|^2 = 16 + 8 + 4
|a + b|^2 = 28
|a + b| = √28 = 2√7