Question

resolva as equações:
a) 3x² = 243
b) 9x² - 81 = 0
c) 5x² + 25 = 525
d) 8x² - 38 = - 30
e) 6x² + 30 = 4x² + 80

Answer 1

a) 3x² = 243 → RESPOSTA ⇔ ${\boxed{\sf \ \red{{\boxed{\sf \ \red{x = +9 ou x = -9}}}}}}$

3x² = 243

x² = 243/3

x² = 81

√x² = √81

x = ±√81

${\boxed{\sf \ \red{{\boxed{\sf \ \red{x = +9 ou x = -9}}}}}}$

b) 9x² - 81 = 0  → RESPOSTA ⇔ ${\boxed{\sf \ \red{{\boxed{\sf \ \red{x=3}}}}}}$

9x2=81

x2=81/9

x2=9

x=√9

${\boxed{\sf \ \red{{\boxed{\sf \ \red{x=3}}}}}}$

c) 5x² + 25 = 525  → RESPOSTA ⇔ ${\boxed{\sf \ \red{{\boxed{\sf \ \red{x=-10, ou, x=10}}}}}$

d) 8x² - 38 = - 30  → RESPOSTA ⇔ ${\boxed{\sf \ \red{{\boxed{\sf \ \red{x=-1, ou, x=1}}}}}}$

e) 6x² + 30 = 4x² + 80  → RESPOSTA ⇔ ${\boxed{\sf \ \red{{\boxed{\sf \ \red{x=-5, ou, x=5}}}}}}$

Answer 2

Explicação passo-a-passo:

a)

$3x^2=243\\ \\ x^2=243\div3\\ \\ x^2=81\\ \\ x=\pm\sqrt{81} \\ \\ x=\pm9\\ \\ S=\{-9,+9\}$

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b)

$9x^2-81=0\\ \\ 9x^2=81\\ \\ x^2=81\div9\\ \\ x^2=9\\ \\ x=\pm\sqrt{9} \\ \\ x=\pm3\\ \\S=\{-3,+3\}$

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c)

$5x^2+25=525\\ \\ 5x^2=525-25\\ \\ 5x^2=500\\ \\ x^2=500\div5\\ \\ x^2=100\\ \\ x=\pm\sqrt{100} \\ \\ x=\pm10\\ \\ S=\{-10,+10\}$

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d)

$8x^2-38=-30\\ \\ 8x^2=-30+38\\ \\ 8x^2=8\\ \\ x^2=8\div8\\ \\ x^2=1\\ \\ x=\pm\sqrt{1} \\ \\ x=\pm1\\ \\ S=\{-1,+1\}$

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e)

$6x^2+30=4x^2+80\\ \\ 6x^2-4x^2=80-30\\ \\ 2x^2=50\\ \\ x^2=50\div2\\ \\ x^2=25\\ \\ x=\pm\sqrt{25} \\ \\ x=\pm5\\ \\ S=\{-5,+5\}$