Question

The number of distinct real roots of the equation $(x+3{)}^4+(x+5{)}^4=16$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

Put $x+4=t$, so that (1) becomes
$(t-1{)}^4+(t+1{)}^4=16$
$\Rightarrow 2\left(t^4+6t^2+1\right)=16$
$\Rightarrow t^4+6t^2-7=0$
$\Rightarrow t^2=1,-7\Rightarrow t=\pm 1,\sqrt{7}i$
Thus, the equation (1) has two real roots.