akar akar persamaan kuadrat x^2 + px + q = 0 adalah a dan b . jika a^2 b + ab^2 = 6 dan a^-1 + b^-1 = 3/2, maka a^2 - b^2 adalah

Persamaan Kuadrat

x² + px + q = 0
a + b = -p
ab = q

a²b + ab² = 6
ab(a + b) = 6
-pq = 6

a^-1 + b^-1 = 3/2
1/a + 1/b = 3/2
(a + b)/ab = 3/2
-p/q = 3/2
-p = 3/2 q

-pq = 6
3/2 q . q = 6
q² = 2 × 6/3
q = 2
-p = 6/q = 3
p = -3

D = p² - 4.1.q = 1
a - b = √D /1 = 1

a² - b²
= (a + b)(a - b)
= -p . √D
= -(-3) . 1
= 3