Ответ(ы) на вопрос:
Гостьa) [latex]x= \frac{4}{x} - \frac{x}{9} +2[/latex]
[latex]x= \frac{4}{x} - \frac{x}{9} +2, x \neq 0[/latex]
[latex]x- \frac{4}{x} + \frac{x}{9} -2=0[/latex]
[latex]\frac{9x+x}{9} - \frac{4}{x} -2=0[/latex]
[latex]\frac{10x}{9} - \frac{4}{x} -2=0[/latex]
[latex]\frac{10x^{2}-36-18x }{9x}=0[/latex]
[latex]10x^{2}-36-18x =0[/latex]
[latex]2(5x^{2}-18-9x) =0[/latex]
[latex]2(5x^{2}-9x-18) =0[/latex]
[latex]2(5x^{2}+6x-15x-18) =0[/latex]
[latex]2(x(5x+6)-3(5x+6)) =0[/latex]
[latex]2(x-3)(5x+6) =0[/latex]
[latex](x-3)(5x+6) =0[/latex]
[latex] \left \{ {{x-3} \atop {5x+6=0}} \right. [/latex]
[latex] \left \{ {{x=3} \atop {x=-1.2}} \right. [/latex]
б) [latex](1+ \frac{1}{x})^{2}= \frac{9}{ x^{2}}[/latex]
[latex](\frac{x+1}{x})^{2}= \frac{9}{ x^{2}}[/latex]
[latex](\frac{x+1}{x})^{2}= \frac{9}{ x^{2}}, x \neq 0[/latex]
[latex]\frac{(x+1)^{2}}{x^{2}}}= \frac{9}{ x^{2}}[/latex]
[latex]\frac{x^{2}+2x+1}{x^{2}}}= \frac{9}{ x^{2}}[/latex]
[latex] x^{2}+2x+1=9[/latex]
[latex] x^{2}+2x+1-9=0[/latex]
[latex] x^{2}+2x-8=0[/latex]
[latex]D=b^{2}-4ac=2^{2}-4*1*(-8)=4+32=36[/latex]
[latex] \left\{{{x=\frac{-2+6}{2} }\atop{x=\frac{-2-6}{2}}}\right. [/latex]
[latex] \left\{{{x=2}\atop{x=-4}}\right. [/latex]
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