F.4 quardratic equation

(1)

x^2 + 2mx - n^2 = 0
x = {-(2m) +/- sqrt[(2m)^2 - 4(1)(n^2)]} / 2(1)
x = [-2m +/- sqrt(4m^2 - 4n^2)] / 2
x = [-2m +/- 2sqrt(m^2 - n^2)] / 2
x = -m +/- sqrt(m^2 - n^2)

(2)

???

2013-09-17 12:46:30 補充：
pqx^2 - (p^2 + q^2)x + pq = 0
x = {-[-(p^2 + q^2)] +/- sqrt{[-(p^2 + q^2)]^2 - 4(pq)(pq)}} / (2pq)
x = {(p^2 + q^2) +/- sqrt[(p^2 + q^2)^2 - 4(pq)^2]} / (2pq)
x = {(p^2 + q^2) +/- sqrt[(p^2)^2 + 2(pq)^2 + (q^2)^2 - 4(pq)^2]} / (2pq)
x = {(p^2 + q^2) +/- sqrt[(p^2)^2 - 2(pq)^2 + (q^2)^2]} / (2pq)

2013-09-17 12:46:36 補充：
x = [(p^2 + q^2) +/- sqrt(p^2 - q^2)^2] / (2pq)
x = [(p^2 + q^2) +/- (p^2 - q^2)] / (2pq)
x = [(p^2 + q^2) + (p^2 - q^2)] / (2pq) or x = [(p^2 + q^2) - (p^2 - q^2)] / (2pq)
x = p / q or x = q / p

Do you miss the equation for question 2.?

2013-09-17 12:00:32 補充：
50418129 ^_^

我本想等她加上補充發問然後再答，豈料你那麼快速～

那麼把重任交給你吧～

=^o^=

2013-09-17 12:02:38 補充：
第一題也可以考慮用配方法(method of completing square)

x² + 2mx - n² = 0

x² + 2mx = n²

x² + 2mx +m² = n² +m²

(x+m)² = n² +m²

x + m = ±√(n² +m²)

x = -m ± √(n² +m²)