Question

Não estou conseguindo resolver o sistema:
a-b=4
a²-b²=5

Answer 1

    $\left\{\begin{array}{II}{a-b=4}\\\\{a^2-b^2=5}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=4+b}\\\\{(4+b)^2-b^2=5}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=4+b}\\\\{4^2+2\times4\times b+b^2-b^2=5}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=4+b}\\\\{16+8b=5}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=4+b}\\\\{8b=5-16}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=4+b}\\\\{8b=-11}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=4+\left(-\dfrac{11}{8}\right)}\\\\{b=-\dfrac{11}{8}}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=4-\dfrac{11}{8}}\\\\{b=-\dfrac{11}{8}}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=\dfrac{4\times8}{8}-\dfrac{11}{8}}\\\\{b=-\dfrac{11}{8}}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=\dfrac{32}{8}-\dfrac{11}{8}}\\\\{b=-\dfrac{11}{8}}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=\dfrac{32-11}{8}}\\\\{b=-\dfrac{11}{8}}\end{array}\right\Leftrightarrow$

$\Leftrightarrow\left\{\begin{array}{II}{a=\dfrac{21}{8}}\\\\{b=-\dfrac{11}{8}}\end{array}\right$

$Resposta: \;(a\;;\;b)=\left(\dfrac{21}{8}\;;\;-\dfrac{11}{8}\right)$

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