If $$ {a^{x}={(x+y+z)^{y}}}, a^{y}=(x+y+z)^{z}  and \ a^{z}=(x+y+z)^{x}$$ then the value of (x +y +z) is

If pq+qr+rp=0 then find the value of $$ {p^{2}\over {p^{2}-qr}}+{q^{2}\over {q^{2}-rp}}+{r^{2}\over {r^{2}-pq}}$$

(x+2y) (x² + 4y² – 2xy) equal to- 

If $$ {x+{1\over x}=\sqrt{3}}$$ then $$ {x^{48}+x^{378\over7}+x^{726\over11}+x^{60}}$$ is equal to

If (a-b)² + (b-c)² + (c-a)² = 0, then find the value of (a³+b³+c³-3abc) ?

If $$ {x+{9\over x}=6}$$  then find the value of $$ {x^{2}+{1\over x^{3}}}$$

If a =500, b=502 and c=504, then the value of a³ +b³ +c³-3abc

If $$ {8x\over{2x^{2}+7x-2}}=1, x>0,$$ then what is the value of of $$ {x^{3}+{1\over x^{3}}}$$ ?