Question

Determine o valor de m na equação x²-2x+m=0, para que x²₁-x²₂ =2 (x₁ e x₂ são as raízes reais da equação)

Answer 1

{[-b +√(b² -4ac)]/2a}² - { {[-b -√(b² -4ac)]/2a}² } = 2

[b² -2b√(b² -4ac) +(b² -4ac)]/4a - [b² +2b√(b² -4ac) +(b² -4ac)]/4a = 2

b² -b² -2b√(b² -4ac) -2b√(b² -4ac) +(b² -4ac) -(b² -4ac) = 4a * 2

-4b√(b² -4ac) = 8a

√(b² -4ac) = -2a/b

[ -(-2) ± (-2a/b)]/(2a)

[2 ± -2/-2]/(2)

[2 ± 1]/2

x' = 3/2

x'' = 1/2

m = x' * x''

m = 3/2 * 1/2

m = 3/4