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

If x+y+z=12 and x^2+y^2+z^2=70, find the value of x^3+y^3+z^3−3xyz .

If a+b+c=1, a^2+b^2+c^2=2,a^3+b^3+ c^3=3, then find the value of a^4+b^4+c^4

Prove a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)