if x+y+z=9, xy+yz+zx =26; find x²+y²+z²
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