Mathematics - Quadratic Equation Question with Solution | TestHub

$(x+1{)}^5=2\left(x^5+1\right)$

$$\begin{array}{rlrl}& \text{ Let }f(x)=\frac{(x+1{)}^5}{\left(x^5+1\right)}(x\ne -1)& \Rightarrow f^{\prime }(x)=\frac{5(x+1{)}^4\left(1-x^4\right)}{{\left(x^5+1\right)}^2}& \Rightarrow x=1\text{ is maximum }\end{array}$$

As, $f(0)=1$ and $f(1)=16$

And ${\lim }_{x\to \pm \infty }f(x)=1\Rightarrow f(x)=2$ has two solutions but given equation has three solutions. because $\mathrm{x}=-1$ included.