Question

Найдите увеличенную в 5 раз сумму корней уравнения

Answer 1

$sqrt{1+2x sqrt{1- x^{2} } } =2-x \ sqrt{(x+ sqrt{1- x^{2} })^2 } =2-x \ |x+ sqrt{1- x^{2}}|=2-x \ \ 1)x+ sqrt{1- x^{2}}=2-x \ 2)x+ sqrt{1- x^{2}}=x-2 \ \ \ 1)x+ sqrt{1- x^{2}}=2-x \ \ sqrt{1- x^{2}}=2-2x textless = textgreater left { {{2-2x geq 0} atop {1- x^{2} =4-8x+4 x^{2} }} right. \ \ left { {{2x leq 2} atop {5 x^{2} -8x+3=0}} right. left { {x leq 1} atop {5 x^{2} -8x+3=0}} right. \ \ 5 x^{2} -8x+3=0 \ \ D=64-4*5*3=64-60=4=2^2$

$x_1= frac{8-2}{2*5} =0.6 \ \ x_2= frac{8+2}{2*5} =1$

$1) left { {{x leq 1} atop {x_1=0.6; x_2=1}} right. textless = textgreater x_1=0.6; x_2=1 \ \ \2) x+ sqrt{1- x^{2}}=x-2 \ sqrt{1- x^{2} } =-2 = textgreater KOPHEI HET \ \ 1) 5(x_1+x_2)= 5(0.6+1)=5*1.6=8 \ \ OTBET: 8$