Question

Se x ≠ 7, x ≠ 2 e $\frac{x - 7}{x - 2} = \frac{x - 2}{x - 7}$ então x é igual a:

Answer 1

$\frac{x-7}{x-2}=\frac{x-2}{x-7}\\ \\ (x-7)^2=(x-2)^2\\ \\ x^2-14x+49=x^2-4x+4\\ \\ -14x+4x=4-49\\ \\ -10x=-45\\ \\ x=\frac{45}{10}\\ \\ x=\frac{9}{2}$

Answer 2

Olá Larissa, basta multiplicar cruzado:

$\dfrac{x-7}{x-2}= \dfrac{x-2}{x-7}\\\\ (x-7)(x-7)=(x-2)(x-2)\\ x^{2} -7x-7x+49= x^{2} -2x-2x+4\\ x^{2} -14x+49= x^{2} -4x+4\\ x^{2} - x^{2} -14x+4x=4-49\\ -14x+4x=-45\\ -10x=-45\\\\ x= \dfrac{-45}{-10}~\to~simplifique~por~5,~numerador~e~denominador:\\\\\\ x= \dfrac{-45:5}{-10:5}~\to~x= \dfrac{9}{2}\\\\\\ S=\left\{ \dfrac{9}{2}\right\}$

Espero ter ajudado e tenha ótimos estudos =))