Step 1

Given equation is

\(\displaystyle{x}^{{{4}}}={16}-{x}^{{{3}}}\)

We need to find all the real solutions, rounded to two decimals.

Step 2

Since there are no easy roots for the equation, we find the real roots graphically.

We plot \(\displaystyle{y}={x}^{{{4}}}\) and \(\displaystyle{y}={16}-{x}^{{{3}}}\) and we graphically calculate the intersection points of these two curves.

Roots are

\(\displaystyle{x}_{{{1}}}={2.31}\)

\(\displaystyle{x}_{{{2}}}={1.79}\)

Given equation is

\(\displaystyle{x}^{{{4}}}={16}-{x}^{{{3}}}\)

We need to find all the real solutions, rounded to two decimals.

Step 2

Since there are no easy roots for the equation, we find the real roots graphically.

We plot \(\displaystyle{y}={x}^{{{4}}}\) and \(\displaystyle{y}={16}-{x}^{{{3}}}\) and we graphically calculate the intersection points of these two curves.

Roots are

\(\displaystyle{x}_{{{1}}}={2.31}\)

\(\displaystyle{x}_{{{2}}}={1.79}\)