Question

Qual é o valor de x – 2 ? pffff ajuda aí esse trabalho vale 4 pontos ..... e vai somar com a prova

Answer 1

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$\boxed{\begin{array}{l}\sf\triangle ABC\sim\triangle AEF\\\sf\dfrac{AB}{AE}=\dfrac{AC}{AF}\\\sf\dfrac{2x+3}{x}=\dfrac{3x+2}{x+2}\\\sf 3x^2+2x=2x^2+7x+6\\\sf 3x^2-2x^2+2x-7x-6=0\\\sf x^2-5x-6=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-5)^2-4\cdot1\cdot(-6)\\\sf\Delta=25+24\\\sf\Delta=49\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-5)\pm\sqrt{49}}{2\cdot1}\\\sf x=\dfrac{5\pm7}{2}\begin{cases}\sf x_1=6\\\sf x_2=-1\end{cases}\\\sf como~x>0,temos~que~x=6\\\sf da\acute i\\\sf x-2=6-2=4\end{array}}$

$\boxed{\begin{array}{l}\sf2~\dfrac{1}{4}=\dfrac{9}{4}~~~~1~\dfrac{1}{2}=\dfrac{3}{2}\\\sf\triangle ABC\sim\triangle AEF\\\sf\dfrac{x+\frac{9}{4}}{x}=\dfrac{\frac{7}{2}}{2}\\\sf 2x+\dfrac{9}{2}=\dfrac{7x}{2}\cdot2\\\sf 4x+9=7x\\\sf 7x-4x=9\\\sf 3x=9\\\sf x=\dfrac{9}{3}\\\sf x=3\\\sf x-2=3-2=1\end{array}}$