Question

√x+5=x-1

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Answer 1

$\sqrt{x+5} =x-1 \to\\\\\\ ( \sqrt{x+5})^2 =(x-1)^2 \to\\\\ x+5= x^{2} -x-x+1\to \\\\ x^{2} -2x+1-x-5=0\to \\\\ x^{2} -3x-4=0\\\\a=1;b=-3;c=-4\\\\\\ \Delta=b^2-4ac\to \Delta=(-3)^2-4.1.(-4)\to \Delta=9+16\to \Delta=25\\\\ x' \neq x''$




$x= \dfrac{-b\pm \sqrt{\Delta} }{2a} \to x= \dfrac{-(-3)\pm \sqrt{25} }{2.1} \to x= \dfrac{3\pm 5 }{2} \to \\\\\\ x'= \dfrac{3+ 5 }{2} \to x'= \dfrac{8 }{2} \to x'=4\\\\\\ x''= \dfrac{3- 5 }{2} \to x''= \dfrac{-2 }{2} \to x''=-1\\\\\\ \boxed{\boxed{S=\{-1;4\} }}$