Question

Алгебра 10 класс (пример на фото)

Answer 1

$(x+1)^5+(x-1)^5=32x\\(x+1)^5+((x-1)^5-32x)=0\\(x+1)^5+(x^5-5x^4+10x^3-10x^2-27x-1)=0\\((x+1)^4+(x^4-6x^3+16x^2-26x-1)(x+1)=0\\((x^4+4x^3+6x^2+4x+1)+(x^4-6x^3+16x^2-26x-1))(x+1)=0\\(x^4+4x^3+6x^2+4x+1+x^4-6x^3+16x^2-26x-1)(x+1)=0\\(2x^4-2x^3+22x^2-22x)(x+1)=0\\2x^4-2x^3+22x^2-22x=0\\x^4-x^3+11x^2-11x=0\\x(x^3-x^2+11x-11)=0\\x=0\\x^3-x^2+11x-11=0\\x^2(x-1)+11(x-1)=0\\(x^2+11)(x-1)=0\\x^2+11=0\\x^2 \neq -11\\x-1=0\\x=1\\x+1=0\\x=-1$