+26367 If then the numerical value of a/b + b/a is equal to x. Find the value of x.
$$\small{\text{$
\begin{array}{rcll}
(a^2 +b^2)^3 &=& (a^3+b^3)^2 \\
(a^2)^3+3\cdot(a^2)^2\cdot (b^2)^1 +3\cdot (a^2)^1\cdot (b^2)^2 + (b^2)^3 &=& (a^3)^2 + 2\cdot(a^3)^1\cdot (b^3)^1 + (b^3)^2\\
a^6+3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 + b^6 &=& a^6 + 2\cdot a^3\cdot b^3 + b^6\\
\not{a^6}+3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 + \not{b^6} &=& \not{a^6} + 2\cdot a^3\cdot b^3 + \not{b^6}\\
3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 &=& 2\cdot a^3\cdot b^3 \\
3\cdot a^4\cdot b^2 +3\cdot a^2\cdot b^4 &=& 2\cdot a^3\cdot b^3 & | \quad : (a^3\cdot b^3) \\
3\cdot\frac{ a }{ b }+3\cdot \frac{ b } { a } &=& 2 \\
3\cdot\frac{ a }{ b }+3\cdot \frac{ b } { a } &=& 2 & | \quad : 3 \\
\frac{ a }{ b }+ \frac{ b } { a } &=& \frac{2}{3}
\end{array}
$}}\\
\mathbf{x=\dfrac{ a }{ b }+ \dfrac{ b } { a } &=& \dfrac{2}{3} }$$
