Answer
$x$ = $5-2\sqrt[4] 5$ and $5+2\sqrt[4] 5$
i.e.
$x$ $\approx$ $2.01$ and $7.99$
Work Step by Step
Given equation is-
$(x-5)^{4}-80$ = $0$
Algebraic Solution:
$(x-5)^{4}-80$ = $0$
i.e. $(x-5)^{4}$ = $80$ = $(±2\sqrt[4] 5)^{4}$
i.e. $x-5$ = $±2\sqrt[4] 5$
i.e. $x$ = $5±2\sqrt[4] 5$
i.e. $x$ = $5-2\sqrt[4] 5$ and $5+2\sqrt[4] 5$
Using calculator-
$x$ $\approx$ $2.01$ and $7.99$
Graphical Solution:
$(x-5)^{4}-80$ = $0$
Now graphing $y$ = $(x-5)^{4}-80$
We get $x-intercepts $ as $2.0093$ and $7.99007$
i.e. $x$ $\approx$ $2.01$ and $7.99$
