Question

equação irracional √x+7 + x=5

Answer 1

$\sqrt{x+7} +x=5$

Restrição: $x+7 \geq 0$ ⇒ $x \geq -7$

$\sqrt{x+7} =5-x$

$(\sqrt{x+7})^{2} =(5-x)^{2}$

$x+7 =25-10x+ x^{2}$

$- x^{2}+10x+ x+7 - 25=0$

$- x^{2}+11x-18=0$  $\times( -1)$

$x^{2}-11x+18=0$

$a=1 b=-11 c=18$

$\Delta= b^{2} -4ac= (-11)^{2} -4.1.18=121-72=49$

$x= \dfrac{-b+ \sqrt{\Delta} }{2a} = \dfrac{-(-11)+ \sqrt{49} }{2.1} = \dfrac{11+ 7 }{2} = \dfrac{18 }{2} =9$
ou
$x= \dfrac{-b- \sqrt{\Delta} }{2a} = \dfrac{-(-11)- \sqrt{49} }{2.1} = \dfrac{11- 7 }{2} = \dfrac{4 }{2} =2$

$S=\{x\in\mathbb{R}\ |\text{ x=2 ou x=9}\}$