If $$x + y + z = 10$$, $$x^3+y^3+z^3=75$$ and $$xyz=15$$, then find the value of $$x^2+y^2+z^2−xy−yz−zx$$

Question

If $$x + y + z = 10$$, $$x^3+y^3+z^3=75$$ and $$xyz=15$$, then find the value of $$x^2+y^2+z^2−xy−yz−zx$$

Uniteasy Admin · Accepted Answer

Using the identity
$$x^3+y^3+z^3−3xyz =  (x+y+z)(    x^2+y^2+z^2−xy−yz−zx)$$
The expression can be expressed
$$x^2+y^2+z^2−xy−yz−zx = \dfrac{x^3+y^3+z^3−3xyz}{x+y+z}  = \dfrac{75-3\cdot  15}{10} =3 $$

Multiple Choice Question (MCQ)

Answer