Question

Resolva cada uma das equações do 2° grau e indique as raízes: a) x² - 225 = 0 b) 4x² - 121 = 0 c) 0,01 x² - 100 = 0 d) -x² + 900 = 0

Answer 1

$\mathtt{a)}~\mathsf{x^2-225=0}\\\mathsf{x^2=225}\\\mathsf{x=\pm\sqrt{225}}\\\mathsf{x=\pm15}\\\mathsf{s=\{-15,15\}}\\\mathtt{b)} ~\mathsf{4x^2-121=0}\\\mathsf{4x^2=121}\\\mathsf{x^2=\dfrac{121}{4}}\\\mathsf{x=\pm\sqrt{\dfrac{121}{4}}}\\\mathsf{x=\pm\dfrac{11}{2}}\\\mathsf{s=\{-\dfrac{11}{2},\dfrac{11}{2}\}}\\\mathtt{c)}~\mathsf{0,01x^2-100=0}\\\mathsf{0,01x^2=100}\\\mathsf{x^2=\dfrac{100}{0,01}}\\\mathsf{x=\pm\sqrt{\dfrac{100}{0,01}}=\pm\dfrac{10}{0,1}=\pm100}\\\mathsf{s=\{-100,100\}}\\\mathtt{d)}\mathsf{-x^2+900=0\implies x^2=900}\\\mathsf{x=\pm\sqrt{900}}\\\mathsf{x=\pm30}\\\mathsf{s=\{-30,30\}}$

Answer 2

Resposta:

a) x

2

−225=0

x

2

=225

x=±

225

x=±15

s={−15,15}

b) 4x

2

−121=0

4x

2

=121

x

2

=

4

121

x=±

4

121

x=±

2

11

s={−

2

11

,

2

11

}

c) 0,01x

2

−100=0

0,01x

2

=100

x

2

=

0,01

100

x=±

0,01

100

=±

0,1

10

=±100

s={−100,100}

d)−x

2

+900=0⟹x

2

=900

x=±

900

x=±30

s={−30,30}

Explicação passo-a-passo:

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