Question

Find all real solutions of the equation X^{4}=16-x^{3}, rounded to two decimals.

Decimals
ANSWERED
asked 2021-08-09
\(\displaystyle{X}^{{{4}}}={16}-{x}^{{{3}}}\) - Find all real solutions of the equation, rounded to two decimals.

Answers (1)

2021-08-10
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.
image
Roots are
\(\displaystyle{x}_{{{1}}}={2.31}\)
\(\displaystyle{x}_{{{2}}}={1.79}\)
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