If a+b+c =9 and ab+bc+ca=23, find the value of a²+b²+c².

If a+b+c =0 and a²+b²+c² =16, find the value of ab + bc + ca.

If a²+b²+c² =16, and ab + bc + ca=10, find the value of a+b+c.

Find the value of 4x²+y²+25z²+4xy-10yz-20zx when x = 4, y = 3 and z = 2.

Simplify each of the following expressions :

(i) (x+y+z)²+

(ii) (x+y-2z)²-x² – y² - 3z²+4xy

(iii) (x² – x + 1)² - (x² + x + 1)²