Question

please show the work, I know the answer I just need the steps. What is the solution of the equation? 3 ^5sqrt(x+2)^3+3=27

Answer 1

The value of x = - 1.7863 (approx) or, $\dfrac{8}{81} ^{\dfrac{2}{3}}}-2$

Step-by-step explanation:

We have,

$3^5\sqrt{(x+2)^3}+3=27$

To find, the value of x in the given equation = ?

∴ $3^5\sqrt{(x+2)^3}+3=27$

⇒ $243\sqrt{(x+2)^3}=27-3$

⇒ $\sqrt{(x+2)^3}=\dfrac{24}{243}$

⇒ ${(x+2)^{\dfrac{3}{2}}}=\dfrac{8}{81}$

⇒ $(x+2)=\dfrac{8}{81} ^{\dfrac{2}{3}}}$

⇒ $x=\dfrac{8}{81} ^{\dfrac{2}{3}}}-2$

⇒ x = 0.2137 - 2

⇒ x = - 1.7863 (approx)

Thus, the value of x = - 1.7863 (approx) or, $\dfrac{8}{81} ^{\dfrac{2}{3}}}-2$.