If a+b+c=15 and a²+b²+c²=83 then the value of a³+b³+c³-3abc

If  $$ \ {xy\over x+y}= a, $$ $${xz\over x+z}=b $$ and $$ {yz\over y+z} =c $$  where a, b, c are all non – zero numbers, then x equals to

Find the minimum value of x which the expression  
x³-7x²+11x - 5 ≥ 0.

If a=x+y, b=x-y, c=x+2y, then $$ {a^2+b^2+c^2}-ab-bc-ca $$ is

Simplification 

If x²+y²+z² = xy + yz + zx, then the value of $${3x^4+7y^4+5z^4}\over{5x^2y^2+7y^2z^2+3z^2x^2} $$ is

If x = 2 then the value of $$ x^3 + 27x^2 + 243x + 631$$ is:

If a\b + b\a =1, then the value of a³+b³ will be