2xkuadrat+3x+1=0 adalah x1 dan x2. susunlah persamaan kuadrat baru yang akar-akarnya 1/x1-2 dan 1/x2-2

By Posted on

2xkuadrat+3x+1=0 adalah x1 dan x2. susunlah persamaan kuadrat baru yang akar-akarnya 1/x1-2 dan 1/x2-2

Foto soalnya ada gak?

Soalnya mana yang bener nih?

frac{1}{x_{1}-2} & frac{1}{x_{2}-2} atau frac{1}{x_{1}}-2 & frac{1}{x_{2}}-2

Rumus persamaan kuadrat baru = x² – (α + β)x + α × β = 0

2x² + 3x +1 = 0

a = 2, b = 3, c = 1

(x_{1} + x_{2}) = frac{-b}{a}

= frac{-3}{2}

(x_{1} * x_{2}) = frac{c}{a}

= frac{1}{2}

Penyelesaian kalo di soal akarnya frac{1}{x_{1}-2} & frac{1}{x_{2}-2}

α + β = frac{1}{x_{1}-2} + frac{1}{x_{2}-2}

= frac{x_{2}-2}{x_{1}x_{2}-2x_{1}-2x_{2}+4} + frac{x_{1}-2}{x_{1}x_{2}-2x_{1}-2x_{2}+4}

= frac{x_{1}+x_{2}-4}{x_{1}x_{2}-2x_{1}-2x_{2}+4}

= frac{frac{-3}{2}-4}{frac{1}{2}-2(frac{1}{2})+4}

= frac{-11}{7}

α × β = frac{1}{x_{1}-2} * frac{1}{x_{2}-2}

= frac{1}{x_{1}x_{2}-2x_{1}-2x_{2}+4}

= frac{1}{frac{1}{2}-2(frac{1}{2})+4}

= frac{2}{7}

Maka, persamaan kuadrat barunya x² + frac{11}{7}x + frac{2}{7} = 0 atau 7x² + 11x + 2 = 0

Penyelesaian kalo di soal akarnya frac{1}{x_{1}}-2 & frac{1}{x_{2}}-2

α + β = frac{1}{x_{1}}-2 + frac{1}{x_{2}}-2

= frac{1}{x_{1}} - frac{2x_{1}}{x_{1}} + frac{1}{x_{2}} - frac{2x_{2}}{x_{2}}

= frac{2x_{1}-1}{x_{1}} + frac{2x_{2}-1}{x_{2}}

= frac{2x_{1}x_{2}-x_{2}}{x_{1}x_{2}} + frac{2x_{1}x_{2}-x_{1}}{x_{1}x_{2}}

= frac{2x_{1}x_{2}-x_{2} + 2x_{1}x_{2}-x_{1}}{x_{1}x_{2}}

= frac{4x_{1}x_{2}-(x_{1} + x_{2})}{x_{1}x_{2}}

= frac{4(frac{1}{2}) + frac{3}{2}}{frac{1}{2}}

= 2(2 + frac{3}{2})

= 7

α × β = (frac{1}{x_{1}}-2) * (frac{1}{x_{2}}-2)

= frac{1}{x_{1}}(frac{1}{x_{2}}-2)-2(frac{1}{x_{2}}-2)

= frac{1}{x_{1}x_{2}}-2(frac{1}{x_{1}}+frac{1}{x_{2}})+4

= frac{1}{x_{1}x_{2}}-2(frac{x_{2}}{x_{1}x_{2}}+frac{x_{1}}{x_{1}x_{2}})+4

= frac{1}{x_{1}x_{2}}-2(frac{x_{1}+x_{2}}{x_{1}x_{2}})+4

= 2 – 2(-3) + 4

= 12

Maka, persamaan kuadrat barunya x² + 7x + 12 = 0

Tanda bintang (*) artinya kali