Question

1)Sem resolver a equação
${ \times }^{2} - \times - 12 = 0$
calcule os valores de:
A)
$(x_{1} + x_{2}) - ( x_{1}. x_{2})$
B)
$( \times _{1} + \times _{2}).( \times _{1}. \times _{2})$
C)
$( \times _{1} + \times _{ 2}) - ( \times _{1}. \times _{2}) {}^{2}$

Answer 1

Olá!!!

Resolução!!

1°)

x² - x - 12 = 0

ax² + bx + c = 0
ax² + Sx + P = 0

x1 + x2 = - b/a = - ( - 1/1 ) = 1/1 = 1
x1 • x2 = c/a = -12/1 = - 12

x1 = 4
x2 = - 3

a)

= ( x1 + x2 ) - ( x1 • x2 )
= ( 4 + ( - 3 ) ) - ( 4 • ( - 3 ) )
= ( 4 - 3 ) - ( - 12 )
= 1 - ( - 12 )
= 1 + 12
= 13

b)

= ( x1 + x2 ) • ( x1 • x2 )
= ( 4 + ( - 3 ) ) • ( 4 • ( - 3 ) )
= ( 4 - 3 ) • ( - 12 )
= 1 • ( - 12 )
= - 12

c)

= ( x1 + x2 ) - ( x1 • x2 )²
= ( 4 + ( - 3 ) ) - ( 4 • ( - 3 ) )²
= ( 4 - 3 ) - ( - 12 )²
= 1 - 144
= - 143

Espero ter ajudado!!!