Question

resolva as equações irracionais a)√x+1=7 b)√7+x=3 c)√2x-4=6 d)∛x+2=2

Answer 1

Resolva as equações irracionais

a)√x+1=7       (lembrando que: (√) = (²)
√x + 1 = 7
x + 1 = 7²
x + 1 = 49
x = 49 - 1
x = 48

 b)√7+x=3      idem acima

√7 + x = 3
7 + x = 3²
7 + x = 9
x = 9 - 7
x = 2
  
c)√2x-4=6  idem acima

√2x - 4 = 6
2x - 4 = 6²
2x - 4 = 36
2x = 36 + 4
2x = 40
x = 40/2
x = 20

 d)∛x+2=2

∛x + 2 = 2                (lembrando que: (∛) = (³))
x + 2 = 2³
x + 2 = 8
x = 8 - 2
x = 6

Answer 2

a)
$\sqrt{x} + 1 = 7 \\ \sqrt{x} = 7 - 1 \\ \sqrt{x} = 6 \\ x = 6^{2} \\ \boxed{x = 36}$

b)
$\sqrt{7} +x = 3 \\ \boxed{x = 3 - \sqrt{7}}$

c)
$\sqrt{2x} - 4 = 6 \\ \sqrt{2x} = 6 +4 \\ \sqrt{2x} = 10 \\ 2x = 10^{2} \\ 2x = 100 \\ x = \frac{100}{2} \\ \boxed{x = 50}$

d)$\sqrt[3]{x} +2 = 2 \\ \sqrt[3]{x} = 2 - 2 \\ \sqrt[3]{x} = 0 \\ x = 0^{3} \\ \boxed{x = 0}$