Question

resolva as equações de 2º grau incompleta sendo x um n° real.
a) 4x²-100=0
b)-2x²+64=0
c)9x²=0
d) x(x-2)=1-2x
e) 3x²/5=0
f) 3x(x+2)=6x

Answer 1

$a) 4x^2-100=0\to \\\\ 4 x^{2} =100\to \\\\ x^{2} = \frac{100}{4} \to \\\\ x^{2} =25\to \\\\ x=+- \sqrt{25} \to \\\\ x=+-5$





$b)-2x^2+64=0\to\\\\ -2x^2=-64\to\\\\ x^{2} \frac{-64}{-2} \to \\\\x^{2} =32\to\\\\ x=+- \sqrt{32} \\\\ x=+-5,65$





$c)9x^2=0\to x^{2} =-9\\\\ x=+- \sqrt{-9} \\\\ x=+- \sqrt{-1*9} \\\\ x=+- \sqrt{-1}* \sqrt{9}\\ \\obs: \sqrt{-1}=i ; \sqrt{9}=3, logo \\\\x=+- \sqrt{-1}* \sqrt{9}= +-3i$





$d) x(x-2)=1-2x\to\\\\ x^{2} -2x=1-2x\to \\\\ x^{2} -2x+2x=1\to \\\\ x^{2} =1\to \\\\x=+- \sqrt{1} \to\\\\ x=+-1$





$e)\frac{3 x^{2} }{5} =0\\\\  \frac{3 x^{2} }{5} = \frac{0}{5} \\\\ 3 x^{2} =0 \\\\ x^{2} =-3\\\\ x= +-\sqrt{-3}\\\\ x= +-\sqrt{-1*3} \\\\x=+- \sqrt{-1} * \sqrt{3} \\\\ x=+-1,7i$





$f) 3x(x+2)=6x\\\\3 x^{2} +6x=6x\\\\3 x^{2} +6x-6x=0\\\\ 3 x^{2} =0\\\\ x^{2} =-3\\\\ x= +-\sqrt{-3}\\\\ x= +-\sqrt{-1*3} \\\\x=+- \sqrt{-1} * \sqrt{3} \\\\ x=+-1,7i$