Question

Dada a função y=x²-5x+2 função definida de R emR, calcule os valores de x tal que f(x) =-4
Me ajudem por favor

Answer 1

y= x² -5x +2

se f(x)=y= -4

x² -5x + 2 + 4=0

x² -5x +6=0

a=1
b=-5
c=6

Δ=b² -4ac
Δ=(-5)²-4(1)(6)
Δ=25-24
Δ=1

$x= \frac{-b\pm \sqrt{\Delta} }{2a} = \frac{~-(-5)\pm \sqrt{1} }{2} = \frac{~5\pm1}{2} \\ \\ x'= \frac{5+1}{2} = \frac{6}{2} =3 \\ \\ x"= \frac{5-1}{2} = \frac{4}{2} =2 \\ \\ ~logo~~x=3~~ou~~x=2$

Answer 2

$y=x^2-5x+2 \\ \\ f(x)=x^2-5x+2 \\ \\ -4=x^2-5x+2 \\ \\ x^2-5x+2+4=0 \\ \\ x^2-5x+6=0 \\ \\ x= \dfrac{-b \pm \sqrt{b^2 -4 \cdot a \cdot c} }{2 \cdot a} \\ \\ x= \dfrac{-(-5) \pm \sqrt{(-5)^2 -4 \cdot 1 \cdot 6} }{2 \cdot 1} \\ \\ x= \dfrac{+5 \pm \sqrt{25-24} }{2} \\ \\ x= \dfrac{+5 \pm \sqrt{1} }{2} \\ \\ x_1= \dfrac{+5 +1 }{2} = \dfrac{+6}{2} =+3 \\ \\ x_2= \dfrac{+5 -1 }{2} = \dfrac{+4}{2} =+2$

Resposta: 2 e 3


Bons estudos!