Jika x1 dan x2 adalah akar-akar persamaan x^2+px+q=0,maka (1/x1-1/x2)^2=...

Jika x1 dan x2 adalah akar-akar persamaan x^2+px+q=0,maka (1/x1-1/x2)^2=…

Jawaban Terkonfirmasi

X₁+x₂ = -b/a
= -p

x₁.x₂ = c/a
= q

$(frac{1}{x_{1}}- frac{1}{x_{2}})^{2}=( frac{x_{2}-x_{1}}{x_{1}.x_{2}})^{2}$

$(frac{1}{x_{1}}- frac{1}{x_{2}})^{2}=frac{(x_{2}-x_{1})^{2}}{(x_{1}.x_{2})^{2}}$

$=frac{x_{2}^{2}-2x_{1}x_{2}+x_{1}^{2}}{(x_{1}.x_{2})^{2}}$

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

$=frac{(-p)^{2}-4q}{(q)^{2}}$

$=frac{p^{2}-4q}{q^{2}}$