Question

Number of real solutions of the equation $x^2+{\left(\frac{x}{x-1}\right)}^2=8$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

$x^2+\frac{x^2}{{(x-1)}^2}=8$

$x^2\left({(k-1)}^2\right)+1)={(x-1)}^{2}8$

$x^4-2x^3-6x^2+16x+8=0$

f'(x)$=3x^3-6x^2-12x+16=0$

$=9x^2-12x-12\Rightarrow 3x^2-4x-4=0$

$3x^2-6x+2x-4=0$

$3x(x-2)+2(x-2)=0$

$(x-2)(3x+1)=0$