Question

dada a função f(x) = 2x² - 3x + 1 calcule. b)x, para que f(x+2) = 1

Answer 1

Explicação passo-a-passo:

$f(x) = 2x^2-3x+1$

temos $f(x+2)=1$

Então

$2.(x+2)^2-3.(x+2)+1=1\\2.(x^2+4x+4)-3x-6=1-1\\2x^2+8x+8-3x-6=0\\2x^2+5x+2=0$

$a=2\\b=5\\c=2$

$x=\frac{-b+-\sqrt{b^2-4.a.c} }{2.a} \\x=\frac{-5+-\sqrt{5^2-4.2.2} }{2.2} \\x=\frac{-5+-\sqrt{25-16} }{4} \\x=\frac{-5+-\sqrt{9} }{4} \\x=\frac{-5+-3 }{4} \\\\x_1=\frac{-5+3 }{4} \\x_1=\frac{-2 }{4} \\x_1=\frac{-1 }{2} \\\\x_1=\frac{-5-3 }{4} \\x_1=\frac{-8 }{4} \\x_1=-2$

$S=(-2,-\frac{1}{2})$