Question

If (x + 8)³ + (2x + 16)³ +(2x + 13)³ = 3(x - 8) + (2x + 16) +(2x + 13), then what is the value of x?

Answer 1

$x_1 = -8.38$    $x_2=-6.75+1.4i$  and  $x_3=-6.75-1.4i$

Step-by-step explanation:

$(x+8)^3+(2x+16)^3+(2x+13)^3=3(x-8)+(2x+16)+(2x+13)$

$\Leftrightarrow x^3 +24x^2+192 x+512+8x^3+192x^2+1536x+4096+8x^3+156x^2+1014x+2197=3x-24+2x+16+2x+13$

$\Leftrightarrow 17x^3 +372x^2+2742x+6805=7x+5$

$\Leftrightarrow 17x^3+372x^2+275x +6800 =0$

$x_1 = -8.38$    $x_2=-6.75+1.4i$  and  $x_3=-6.75-1.4i$