Question

Решите уравнение: (х²-1)²+(x²-6x-7)²=0

Answer 1

$(x^2-1)^2+(x^2-6x-7)^2=0\\\\(\, (x-1)(x+1)\, )^2+(\, (x+1)(x-7)\, )^2=0\\\\(x-1)^2(x+1)^2+(x+1)^2(x-7)^2=0\\\\(x+1)^2\cdot (\, (x-1)^2+(x-7)^2\, )=0\\\\1)\; \; (x+1)^2=0\; \; \to \; \; x=-1\\\\2)\; \; (x-1)^2+(x-7)^2=0\\\\x^2-2x+1+x^2-14x+49=0\\\\2x^2-16x+50=0\, |:2\\\\x^2-8x+25=0\\\\D=64-100=-36\ \textless \ 0\; \; \to \; \; net\; kornej\\\\Otvet\; \; x=-1.$