Question

Помогите пожалуйста решить под цифрами 5) 6) 7) и 8)

Answer 1

$5); ; sqrt{x^2-9}=3x-11; ; Rightarrow ; ; left { {{3x-11geq 0} atop {x^2-9=9x^2-66x+121}} right. ; ; left { {{xgeq 11/3} atop {8x^2-66x+130=0}} right. \\left { {{ODZ:; ; xgeq 3frac{2}{3}} atop {4x^2-33x+65=0}} right. \\D/4=49; ,x_1=frac{33-7}8}=frac{13}{4}=3,25; notin ODZ;; ;; ; x_2=frac{33+7}{8}=5\\Otvet:; ; x=5.\\6); ; sqrt{x^2+5x+1}=2x-1; ; Rightarrow ; ; left { {{2x-1geq 0} atop {x^2+5x+1=4x^2-4x+1}} right. ; ; left { {{xgeq 0,5} atop {3x^2-9x=0}} right.$

$left { {{xgeq 0,5} atop {3x(x-3)=0}} right. ; ; left { {{xgeq 0,5} atop {x_1=0; ,; x_2=3}} right. ; ; Rightarrow ; ; x=3; ; (x_1=0notin ODZ)\\Otvet:; ; x=3; .\\7); ; sqrt{x^2-9}=x^2-21; ; Rightarrow ; ; left { {{x^2-21geq 0} atop {x^2-9=x^4-42x^2+441}} right. ; ; left { {{(x-sqrt{21})(x+sqrt{21})geq 0} atop {x^4-43x^2+450=0}} right. \\a); x^4-43x^2+450=0; ,; ; D=49; ,; ; x_1=frac{43-7}{2}=18; ,; ; x_2=frac{43+7}{2}=25\\b); ; (x-sqrt{21})(x+sqrt{21})geq 0; ; ,; ; ; +++(-sqrt{21})---(sqrt{21})+++\\xin (-infty ,-sqrt{21}, ]cup [, sqrt{21},+infty )\\x_1,x_2in (-infty ,-sqrt{21}, ]cup [sqrt{21},+infty )\\Otvet:; ; x=18; ,; x=25; .$

$8); ; sqrt{x^2-1}=sqrt3; ; Rightarrow ; ; left { {{x^2-1geq 0} atop {x^2-1=3}} right. ; ; left { {{xin (-infty ,-1, ]cup [, 1,+infty )} atop {x^2=4}} right. \\left { {{xin (-infty ,-1, ]cup [, 1,+infty )} atop {x_1=-2; ,; x_2=2}} right. \\x_1; ,; x_2in ODZ\\Otvet:; ; x_1=-2; ,; x_2=2; .$

Answer 2

спасибо огромное