Question

URGENTE!

O quadrado de um número diminuído de seu dobro é 15. Calcule esse número.​

Answer 1

$\boxed{\begin{array}{l}\sf n\acute umero:x\\\sf quadrado~do~n\acute umero:x^2\\\sf dobro~do~n\acute uero:2x\\\sf equac_{\!\!,}\tilde ao: x^2-2x=15\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf x^2-2x=15\\\sf x^2-2x-15=0\\\sf \Delta=b^2-4ac\\\sf\Delta=(-2)^2-4\cdot1\cdot(-15)\\\sf\Delta=4+60\\\sf\Delta=64\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-(-2)\pm\sqrt{64}}{2\cdot1}\\\sf x=\dfrac{2\pm8}{2}\begin{cases}\sf x_1=\dfrac{2+8}{2}=\dfrac{10}{2}=5\\\sf x_2=\dfrac{2-8}{2}=-\dfrac{6}{2}=-3\end{cases}\\\sf S=\{5,-3\}\\\sf o~n\acute umero~procurado~\acute e~5~ou\!~-3\end{array}}$