b. 1/x²1 + 1/x²2
c. x1/x2+x2/x1
tolong bantu jawab
Akar akar persamaan kuadrat 3x²-2x-6= 0 adalah x1dan x2 tanpa mencari akar akarnya terlebih dahulu hitunglah: a. 1/x1-1/x2
Jawaban Terkonfirmasi
3x² – 2x – 6= 0
a= 3 , b = -2, c = – 6
x₁+x₂ = -b/a = 2/3
x₁x₂ = ca/ = -6/3 = -2
a) 1/x₁ + 1/x₂ = (x₁+x₂)/(x₁x₂) = (2/3) /(-2) = – 1/3
b) 1/x₁² + 1/x₂² = (x₁²+x₂²) /(x₁x₂)² = [(x₁+x₂)²- 2(x₁x₂)] /(x₁x₂)²
= [(2/3)² -2(-2)] / (-2)²
= (4/9 + 4) /(4)
= 10/9
c)x₁/x₂ + x₂/x₁ =(x₁²+x₂²) /(x₁x₂)= (x₁+x₂)²- 2(x₁x) /(x₁x₂)
= [(2/3)² – 2(-2)]/ (-2)
= (4/9 +4) / (-2)
= - 20/9