Question

Na equação irracional abaixo, determine o valor de x

Answer 1

Resposta:

x=245

Explicação passo-a-passo:

$\sqrt{2\sqrt{10x+50}}=10\\(\sqrt{2\sqrt{10x+50}})^{2}=(10)^{2}\\2\sqrt{10x+50}}=100\\\sqrt{10x+50}}=\frac{100}{2}\\\sqrt{10x+50}}=50\\(\sqrt{10x+50}})^{2}=50^{2}\\10x+50=2500\\10x=2500-50\\10x=2450\\x=\frac{2450}{10} \\x=245$

Answer 2

$\sqrt{2 \sqrt{10x + 50} } = 10 \\ {(\sqrt{2 \sqrt{10x + 50} } )}^{2} = {10}^{2} \\ 2 \sqrt{10x + 50} = 100$

$\sqrt{10x + 50} = \frac{100}{2} \ \\ \sqrt{10x + 50} = 50 \\ {( \sqrt{10x + 50} )}^{2} = {50}^{2} \\ 10x + 50 = 2500$

$10x = 2500 - 50 \\ 10x = 2450 \\ x = \frac{2450}{10} \\ x = 245$