Practicing Success
The product of the roots of the equation $\sqrt[3]{8+x}+\sqrt[3]{8-x}=1$, is ______. |
-189 |
We have, $\sqrt[3]{8+x}+\sqrt[3]{8-x}=1$ $(\sqrt[3]{8+x}+\sqrt[3]{8-x})^3=(1)^3$ [On cubing both sides] $⇒8+x+8-x+3(64-x^2)^{1/3}(\frac{\sqrt[3]{8+x}+\sqrt[3]{8-x}}{1})=1$ $⇒16+3(64-x^2)^{1/3}=1$ $⇒15=-3(64-x^2)^{1/3}$ $⇒(64-x^2)^{1/3}=-5$ $⇒64-x^2=-125 ⇒x^2=189 ⇒ x=± 3\sqrt{21}$ Product of roots = $3\sqrt{21} × - 3\sqrt{21}=-189$ |