Verified Answer :

First, we must expand  and simplify :
\(x + y+z = 9\)

\((x + y+z)^{2} = (9)^{2}\)

\(x^{2} + y^{2}+z^{2} + 2(xy + yz+zx) = 81\)

And Than, Enter the value :

\(x^{2} + y^{2}+z^{2} + 2(26) = 81\)

\(x^{2} + y^{2}+z^{2} + 52 = 81\)

\(x^{2} + y^{2}+z^{2} = 81- 52\)

\(\boxed{x^{2} + y^{2}+z^{2} = 29}\)

we know,
(x + y + z)² = x² + y² + z² + 2(xy + yz + xz)
9²  = x² + y² + z² + 2 X 26
 81 = x² + y² + z² + 52       
81 - 52 = x² + y² + z²
therefore, x² + y² + z² = 29