Question

(x-5)²=1 me ajudem por favor

Answer 1

$(x-5)^2=1\to (x-5)*(x-5)\to \\\\ x^2-10x+25-1=0\to \\\\x^2-10x+24=0\\\\ a=1;\ b=-10;\ c=24\\\\\\ \Delta=b^2-4ac\to \Delta=(-10)^2-4*1*24\to \Delta=100-96\to \Delta=4\\ x' \neq x''\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-10)\pm \sqrt{4} }{2*1} \to x= \frac{10\pm 2 }{2} \to \\\\ x'= \frac{10+ 2 }{2} \to x'= \frac{1 2 }{2} \to x'=6\\\\ x''= \frac{10- 2 }{2} \to x''= \frac{8 }{2} \to x''=4\\\\\\ S=\{4;6\}$