Question

Розвяжіть рівняння! ​

Answer 1

$\displaystyle \sqrt{2x+7}-\sqrt{2-x}=2\\\sqrt{2x+7}=2+\sqrt{2-x}\\2x+7=4+4\sqrt{2-x}+2-x\\2x+7=6+4\sqrt{2-x}-x\\-4\sqrt{2-x}=6-x-2x-7\\-4\sqrt{2-x}=-1-3x\\16(2-x)=1+6x+9x^2\\32-16x=1+6x+9x^2\\32-16x-1-6x-9x^2=0\\31-22x-9x^2=0\\-9x^2-22x+31=0\\9x^2+22x-31=0\\9x^2+31x-9x-31=0\\x(9x+31)-(9x+31)=0\\(9x+31)(x-1)=0\\9x+31=0,x-1=0\\\\ x=-\frac{31}{9},x=1 \\\\ \sqrt{2*(-\frac{31}{9}+7 }-\sqrt{2-(-\frac{31}{9}) }=2, \sqrt{2*1+7}-\sqrt{2-1}=2 \\\\ -2=2, 2=2\\\\ x\neq -\frac{31}{9}, x=1\\\\ x=1$