(3x-1) elevado ao quadrado + (x-2) elevado ao quadrado = 25 Me ajudem... As raízes devem ser -1 e 2.... Pergunta de ideia deAntoniomagalhaes3

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Antoniomagalhaes3 @Antoniomagalhaes3

December 2019 2 26 Report

(3x-1) elevado ao quadrado + (x-2) elevado ao quadrado = 25

Me ajudem... As raízes devem ser -1 e 2.

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Lista de comentários

PauloLuis (3x - 1)² + (x - 2)² = 25
(3x)² - 2.3x.1 - 1² + x² - 2.x.2 - 2² = 25
9x² - 6x + 1 + x² - 4x + 4 = 25
10x² - 10x - 20

Δ = b² - 4.a.c
Δ = -10² - 4 . 10 . -20
Δ = 100 - 4. 10 . -20
Δ = 900

Há 2 raízes reais.

x = (-b +- √Δ)/2a

x' = (--10 + √900)/2.10
x'' = (--10 - √900)/2.10

x' = 40 / 20
x'' = -20 / 20

x' = 2
x'' = -1

1 votes Thanks 2

Comentários (1) (3x-1)²+(x-2)²=25
(3x-1).(3x-1)+(x-2).(x-2)-25=0
9x²-3x-3x+1+x²-2x-2x+4-25=0
10x²-6x-4x+1+4-25=0
10x²-10x-20=0

/\=(-10)²-4.10.(-20)
/\=100+800
/\=900

x'= -(-10)+30/20
x'=10+30/20
x'=40/20
x'=2

x"= -(-10)-30/20
x"=10-30/20
x"= -20/20
x"= -1

S={2,-1}

1 votes Thanks 2