Question

решите срочно, номер 618!!! плиз очень надо

Answer 1

$1)quad sqrt{x+sqrt{6x-9}}+sqrt{x-sqrt{6x-9}}=sqrt6; ,\\(x+sqrt{6x-9)}+2sqrt{x^2-(6x-9)}+(x-sqrt{6x-9})=6\\2x+2sqrt{x^2-6x+9}=6; |:2\\x+sqrt{(x-3)^2}=3\\|x-3|=3-x; ; verno; pri; x-3leq 0,xleq3\\ODZ:; a); 6x-9 geq 0; ; to ; ; x geq frac{3}{2}; ;\\b); x+sqrt{6x-9} geq 0; to ; ; sqrt{6x-9} geq -x; to ; ;  left { {{-x leq 0} atop {6x-9 geq 0}} right.  to$

$left { {{x geq 0} atop {x geq frac{3}{2}}} right. ; to ; ; x geq frac{3}{2}quad ili\\ left { {{-x geq 0} atop {6x-9 geq x^2}} right.;  left { {{x leq 0} atop {x^2-6x+9 geq 0}} right.;  left { {{x leq 0} atop {(x-3)^2 geq 0}} right.; to ; x leq 0\\c); x-sqrt{6x-9} geq 0; to ; ; sqrt{6x-9} leq x; ; to ;  left { {{x geq frac{3}{2}} atop {6x-9 leq x^2}} right. \\ left { {{x geq frac{3}{2}} atop {(x-3)^2 leq 0}} right. ; ; net; reshenij$

$xgeq frac{3}{2}$

Ответ:  х=3/2.
$2)quad sqrt{x+sqrt{x+11}}+sqrt{x-sqrt{x+11}}=4\\x+sqrt{x+11}+2sqrt{x^2-(x+11)}+x-sqrt{x+11}=16\\2x+2sqrt{x^2-x-11}=16\\sqrt{x^2-x-11}=8-x\\x^2-x-11=(8-x)^2\\x^2-x-11=x^2-16x+64\\15x=75\\x=5\\Proverka:; ; sqrt{5+sqrt{16}}+sqrt{5-sqrt{16}}=sqrt{5+4}+sqrt{5-4}=\\=sqrt9+sqrt1=3+1=4\\Otvet:; ; x=5.$