Question

Dependendo do valor de x a sequência (-2, X+ 1. - 4x + 2) será uma P.G. Determine o menor valor de x. é urgente por favor me ajuda

a) 10/4
b)-1/2
c)5
d)-2
e)1​

Answer 1

$\Large\boxed{\begin{array}{l}\sf (x+1)^2=-2\cdot(-4x+2)\\\sf x^2+2x+1=8x-4\\\sf x^2+2x-8x+1+4=0\\\sf x^2-6x+5=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-6)^2-4\cdot1\cdot5\\\sf\Delta=36-20\\\sf\Delta=16\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-6)\pm\sqrt{16}}{2\cdot1}\\\\\sf x=\dfrac{6\pm4}{2}\begin{cases}\sf x_1=\dfrac{6+4}{2}=\dfrac{10}{2}=5\\\\\sf x_2=\dfrac{6-4}{2}=\dfrac{2}{2}=1\end{cases}\\\\\sf o\,menor\,valor\,de\,\,x\,\acute e\,1\end{array}}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf\dagger\maltese~alternativa~e}}}}$