Level: SULIT
Jika a, b, dan c adalah 3 akar yang memenuhi persamaan 5x³ - 12x² + 14x - 2=0, maka tentukan nilai ((a²+b²+c²)/(3ab + 3bc + 3ac)) × (1/a + 1/b + 1/c)!!
Pake cara ya harus,
Ga ada cara ya hapus :)
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Jawaban:
[Suku Banyak]
[Polinomial]
Penjelasan dengan langkah-langkah:
5x³-12x²+14x-2=0
Rumus:
x₁+x₂+x₃=-b/a
x₁.x₂+x₁.x₃+x₂.x₃=c/a
x₁.x₂.x₃=-d/a
x₁+x₂+x₃=-(-12)/5
=12/5
x₁.x₂+x₁.x₃+x₂.x₃=14/5
x₁.x₂.x₃=-(-2)/5
=2/5
a²+b²+c²=>
x₁²+x₂²+x₃²=(x₁+x₂+x₃)²-2(x₁.x₂+x₁.x₃+x₂.x₃)
=(12/5)²-2(14/5)
=(144/25)-(28/5)
=(144/25)-(140/25)
=(4/25)
(3ab+3bc+3ac)=>3(x₁x₂+x₂.x₃+x₁.x₃)
=3(14/5)
=(42/5)
1/a+1/b+1/c=>(1/x₁+1/x₂+1/x₃)
= x₂x₃+x₁x₃+x₁x₂
x₁x₂x₃
= (14/5)
(2/5)
= (14/5)x(5/2)
= 14/2
= 7
[ (a²+b²+c²) ] x [1/a+1/b+1/c]
[(3ab+3bc+3ac)]
[(4/25)] x 7
[(42/5)]
[4/25] x [5/42] x 7
[4/5] x [1/42] x 7
[4/210] x 7
[28/210]
[4/30]
[2/15] [✓]
Detail Jawaban:
Mapel : Matematika
Kelas : 11 / [XI] SMA
Materi : Suku Banyak [ Polinomial ]
Kode Kategorisasi : -
Kata Kunci : Suku Banyak [Polinomial]
Demikian
Semoga bermanfaat dan bermanfaat!
semoga bermanfaat............
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