Preciso de ajuda nessas duas contas: A) x + = B) x + = 7.... Pergunta de ideia deBruno1470

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Preciso de ajuda nessas duas contas:

A) x + $\frac{1}{x}$ = $\frac{5}{2}$

B) x + $\frac{1}{x-5}$ = 7

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MATHSPHIS A)

$x+\frac{1}{x}=\frac{5}{2}\\
\\
2x^2+2=5x\\
\\
2x^2-5x+2=0\\
\\
\Delta=(-5)^2-4.2.2=25-16=9\\
\\
x=\frac{5\pm\sqrt9}{4}\\
\\
x=\frac{5\pm3}{4}\\
\\
x_1=\frac{1}{2}\\
\\
x_2=2
$

b)

$x+\frac{1}{x-5}=7\\
\\
x(x-5)+1=7(x-5)\\
\\
x^2-5x=7x-35\\
\\
x^2-5x-7x+35=0\\
\\
x^2-12x+35=0\\
\\
\Delta=(-12)^2-4.1.35=144-140=4\\
\\
x=\frac{12\pm2}{2}\\
\\
x_1=5\\
\\
x_2=7$

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