Question

√7x-3=x+1 resposta e verificação por favor

Answer 1

Primeiramente, quando você quiser fazer $\sqrt{7x-3}$, escreva √(7x-3) e não √7x-3

$\sqrt{7x-3} = x+1\\\\(\sqrt{7x-3})^2 = (x+1)^2\\\\7x-3= (x+1)^2\\\\7x-3= x^2+2x+1\\\\x^2+2x+1 = 7x-3\\\\x^2+2x-7x+1+3 = 0\\\\x^2-5x + 4 = 0$

Bhaskara:

$x^2-5x + 4 = 0\\\\x = \frac{-b\pm\sqrt{-4ac+b^2}}{2a}\\\\x = \frac{-(-5)\pm\sqrt{-4\times1\times4+(-5)^2}}{2\times1}\\\\x = \frac{5\pm\sqrt{9}}{2}\\\\x = \frac{5\pm3}{2}\\\\x_1 = \frac{5+3}{2} = \frac{8}{2} = 4\\\\x_2 = \frac{5-3}{2} = \frac{2}{2} = 1$

Resposta: x = 4 e x = 1

Verificando:

x = 4

$\sqrt{7x-3} = x+1\\\sqrt{7\times4-3} = 4+1\\\sqrt{28-3} = 5\\\sqrt{25} = 5\\5 = 5$

x = 1

$\sqrt{7x-3} = x+1\\\sqrt{7\times1-3} = 1+1\\\sqrt{7-3} = 2\\\sqrt{4} = 2\\2 = 2$