Thank you for reporting, we will resolve it shortly
Q.
The number of distinct real roots of the equation
$(x+3)^4+(x+5)^4=16$
is
Complex Numbers and Quadratic Equations
Solution:
Put $x+4=t$, so that (1) becomes
$ (t-1)^4+(t+1)^4=16 $
$\Rightarrow 2\left(t^4+6 t^2+1\right)=16 $
$\Rightarrow t^4+6 t^2-7=0 $
$\Rightarrow t^2=1,-7 \Rightarrow t= \pm 1, \sqrt{7} i$
Thus, the equation (1) has two real roots.