(A) $\left(x+\frac{1}{x}\right)^2=2$$(x)^2+\left(\frac{1}{x}\right)^2+2 \times x \times \frac{1}{x}=2$$x^2+\frac{1}{x^2}+2=2$$x^2+\frac{1}{x^2}=0$$\frac{x^4+1}{x}=0$$x^4+1=0$Here, the degree of $x^4+1=0$ is 4.It is not a quadratic equation.(B) $(x-\sqrt{x})^2+2x\sqrt{x}=0$$(x)^2+(\sqrt{x})^2-2 \times x \times \sqrt{x}+2x\sqrt{x}=0$$x^2+x-2x\sqrt{x}+2x\sqrt{x}=0$$x^2+x=0$It is not a quadratic equation because it is not a equation form.(c) $(x+1)^3=(1-x)^3$$(x)^3+3 \times x \times 1(x+1)+(1)^3=(1)^3-(x)^3-3 \times 1 \times x(1-x)$$x^3+3x(x+1)+1=1-x^3-3x(1-x)$$x^3+3x^2+3x+1=1-x^3-3x+3x^2$$x^3+x^3+3x^2-3x^2+3x+3x+1-1=0$$x^3+6x=0$Here, the degree of $x^3+6x=0$ is 3It is not a quadratic equation.(D) $(\sqrt{x}+1)^2=x^2$$(\sqrt{x})^2+(1)^2+2 \times \sqrt{x} \times 1=x^2$$x+1+2\sqrt{x}=x^2$$x^2-x-2\sqrt{x}+1=0$Here, the degree of $x^2-x-2\sqrt{x}+1=0$ is 2 .It is a quadratic equation.