Question

10 kласс примеры. самостоятельная (√5x+1 =3)

Answer 1

$1)\sqrt{5x+1} =3\\5x+1=9\\5x=8\\\\x=\frac{8}{5} =1\frac{3}{5} \\\\2)\sqrt{2x+3} =x\\2x+3=x^2\\-x^2+2x+3=0\\D=\sqrt{2^2-4(-1)*3} =\sqrt{16} =б4\\\\x_1=\frac{-2+4}{-2} =-1\\\\x_2=\frac{-2-4}{-2}=3\\\\3)x+1=\sqrt{8-4x}\\x^2+2x+1=8-4x\\x^2+6x-7=0\\D=\sqrt{6^2-4*1*(-7)} =\sqrt{64} =б8\\\\x_1=\frac{-6+8}{2} =1\\\\x_2=\frac{-6-8}{2} =-7\\\\$$x=1\\\\4)\sqrt{7x+1}[tex]=\sqrt{3x+4} \\7x+1=3x+4\\4x=3\\\\x=\frac{3}{4} \\\\5)\sqrt{x+17} -\sqrt{x+1} =2\\\sqrt{x+17} =2+\sqrt{x+1} \\x+17=4+4\sqrt{x+1} +x+1\\-4\sqrt{x+1} =-12\\\sqrt{x+1}=3\\ x+1=9\\x=8\\\\6)\sqrt{1-x} -\sqrt{13+x} =\sqrt{x+4} \\1-x-2\sqrt{(1-x)(13+x)} +13+x=x+4\\14-x-2\sqrt{13-12x-x^2} =4\\-2\sqrt{13-12x-x^2}=-10+x\\4(12-12x-x^2)=x^2-20x+100\\52-48x-4x^2=x^2-20x+100\\-5x^2-28x-48=0\\D=\sqrt{(-28)^2-4(-5)(-48)} =\sqrt{-176}$