Question

Resolva as equações literais de segundo grau, na incognita x, sendo U=R
a) 4x²-3ax-a²= 0
b) x²+ax-20a²=0

Answer 1

a) 4x²-3ax-a²=0

∆=(-3a)²-4.4.(-a²)

∆=9a²+16a²=25a²

$x = \frac{3a±5a}{8} \\ x1 = \frac{3a + 5a}{8} = \frac{8a}{8} = a \\ x2 = \frac{3a - 5a}{8} = - \frac{2a}{8} = - \frac{a}{4}$

b) x²+ax-20a²=0

∆=a²-4.1.(-20a²) =a²+80a²=81a²

$x = \frac{ - a ±9a }{2} \\ x1 = \frac{ - a + 9a}{2} = \frac{8a}{2} = 4a$

$x2 = \frac{ - a - 9a}{2} = - \frac{10a}{2} = - 5a$