[tex]\sqrt{1+\sqrt{2x-x^2}}+\sqrt{1-\sqrt{2x-x^2}}=2(x-1)^4.(2x^2-4x+1)\\\\ <=> \sqrt{1+\sqrt{2x-x^2}}+\sqrt{1-\sqrt{2x-x^2}}=2.(x^2-2x+1)^2.[1-2.(2x-x^2)]\\\\ \sqrt{2x-x^2}=m\\\\ => pt <=> \sqrt{1+m}+\sqrt{1-m}=2.(1-m^2)^2.(1-2m^2)\\\\ <=> 2+2\sqrt{1-m^2}=4.(1-m^2)^4.(1-2m^2)^2\\\\ \sqrt{1-m^2}=a\\\\ pt <=> 2+2a=4.a^8.(2a^2-1)^2\\\\ <=> 4a^8.(4a^4-4a^2+1)=2a+2\\\\ <=> 16a^{12}-16a^{10}+4a^8-2a-2=0\\\\ <=> 16a^{12}-16a^{11}+16a^{11}-16a^{10}+4a^8-4a^7+4a^7-4a^6+4a^6-4a^5+4a^5-4a^4+4a^4-4a^3+4a^3-4a^2+4a^2-4a+2a-2=0\\\\ <=> (a-1).(16a^{11}+16a^{10}+4a^7+4a^6+4a^5+4a^3+4a^2+4a+2)=0\\\\ <=> a=1\\\\ <=> \sqrt{1-m^2}=1\\\\ <=> m^2=0 <=> m=0\\\\ <=> 2x-x^2=0\\\\ <=>....[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
