Question

Решите уравнение (из интернет урока)

Answer 1

$\displaystyle \sqrt{5-x}-\sqrt{x+4}=3\\\sqrt{5-x}=3+\sqrt{x+4}\\5-x=9+6\sqrt{x+4}+x+4\\5-x=13+6\sqrt{x+4}+x\\-6\sqrt{x+4}=13+x-5+x\\-6\sqrt{x+4}=8+2x\\3\sqrt{x+4}=-4-x\\9(x+4)=16+8x+x^2\\9(x+4)=(4+x)^2\\9(x+4)-(4+x)^2=0\\(x+4)(9-(4+x))=0\\(x+4)(9-4-x)=0\\(x+4)(5-x)=0\\x+4=0,5-x=0\\x=-4,x=5\\\sqrt{5-(-4)}-\sqrt{-4+4}=3,\sqrt{5-5}-\sqrt{5+4}=3\\x=-4,x\neq 5\\x=-4$