Question

Sejam A= 2-raíz de 3 e B= 2/3 -0,444
Determine o valor de 4A + 3B

Answer 1

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$\large\boxed{\begin{array}{l}\sf x=0,444....\cdot10\\\sf 10x=4,444...\\-\underline{\begin{cases}\sf10x=4,444....\\\sf x=0,444\end{cases}}\\\sf 9x=4\\\sf x=\dfrac{4}{9}\\\sf B=\dfrac{2}{3}-0,444....\\\sf B=\dfrac{2}{3}-\dfrac{4}{9}=\dfrac{6-4}{9}\\\sf B=\dfrac{2}{9}\\\sf 4A+3B=4\cdot(2-\sqrt{3})+\diagup\!\!\!3\cdot\dfrac{2}{\diagup\!\!\!9_3}\\\sf 4A+3B=8-4\sqrt{3}+\dfrac{2}{3}\\\sf 4A+3B=\dfrac{24-12\sqrt{3}+2}{3}\\\sf 4A+3B=\dfrac{26-12\sqrt{3}}{3}\end{array}}$