Question

*ME AJUDEM*

Resolva as equações

a) X²-9/16=O

b) 81X² -49=0

c)X²+7x=0

d )3x²-18x=0

e) x²=x

f) 2x²-9x=0

Answer 1

Letra a) x1= -3, x2= 3

Letra b) x1= -7/9, x2= 7/9

Letra c) x1= -7, x2=0

Letra d) x1= 0, x2= 6

Letra e) x1= 0, x2= 1

Letra f) x1= 0, x2= 9/2

Bons estudos!

Answer 2

Explicação passo-a-passo:

$a)\\ x^{2} - \frac{9}{16} = 0 \\x^{2} = \frac{9}{16}\\x = \frac{+}{-} \sqrt{\frac{9}{16} } \\x= - \frac{\sqrt{9} }{\sqrt{16} } = - \frac{3}{4} , x= \frac{\sqrt{9} }{\sqrt{16} } = \frac{3}{4}\\\\b)\\81 x^{2} - 49= 0 \\81x^{2} = 49\\x^{2} = \frac{49}{81} \\x^{2} = \frac{+}{-}\sqrt{ \frac{49}{81}} \\x= - \frac{\sqrt{49} }{\sqrt{81} } = - \frac{7}{9} , x= \frac{\sqrt{49} }{\sqrt{81} } = \frac{7}{9}$

$c) \\x^{2} +7x=0\\\\x_{}=\frac{-7\pm \sqrt{7^2-4\cdot \:1\cdot \:0}}{2\cdot \:1}\\\\x_{}=\frac{-7\pm \:7}{2\cdot \:1}\\\\x_1=\frac{-7+7}{2\cdot \:1},\:x_2=\frac{-7-7}{2\cdot \:1}\\\\x=0,\:x=-7$

$\\d)\\3x^{2} -18x=0\\x_{1,\:2}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\cdot \:3\cdot \:0}}{2\cdot \:3}\\\\x_{1,\:2}=\frac{-\left(-18\right)\pm \:18}{2\cdot \:3}\\\\x_1=\frac{-\left(-18\right)+18}{2\cdot \:3},\:x_2=\frac{-\left(-18\right)-18}{2\cdot \:3}\\\\x_1=6,\:x_2=0$

$e)\\x^{2} = x \\x^{2} -x = 0\\\\x_{}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:0}}{2\cdot \:1}\\\\x_1=\frac{-\left(-1\right)+1}{2\cdot \:1},\:x_2=\frac{-\left(-1\right)-1}{2\cdot \:1}\\\\x=1,\:x=0$

$\\f)\ 2x^{2} -9x=0\\\\x_{1,\:2}=\frac{-\left(-9\right)\pm \sqrt{\left(-9\right)^2-4\cdot \:2\cdot \:0}}{2\cdot \:2}\\\\x_{1,\:2}=\frac{-\left(-9\right)\pm \:9}{2\cdot \:2}\\\\x_1=\frac{-\left(-9\right)+9}{2\cdot \:2},\:x_2=\frac{-\left(-9\right)-9}{2\cdot \:2}\\\\x_1=\frac{9}{2},\:x_2=0$