$$ {1\over {^3\sqrt{4}+{^3\sqrt{2}}}+1}=a^3\sqrt{4}+ b^3\sqrt{2}+c $$ and a, b, c are rational numbers, then a + b + c is equal to

If p, q, r are all real numbers, then (p – q)³ + (q – r)³ + (r – p)³ is equal to 

If a + b + c = 6, a³ + b³+c³-3abc=342, then what is the value of ab + bc + ca?

if $${{x^{24}+1}\over x^{12}}=7$$ then the value of   $${{x^{72}+1}\over x^{36}}$$ is

If 27(x+y)³ – 8(x-y)³=(x+5y)(Ax²+By²+Cxy), then what is the value of (A+B-C)?

If x = 19 and y = 18, then the value of   $$ {{x^2}+{y^2}+{xy}}\over x^3-y3 $$ is

$$4a-{4\over a}+3=0$$ then the value of :   $$ a^3-{1\over a^3}+3=?$$

if $$m+{1\over(m-2)}=4$$,then find the value of  $$ (m-2)^2+ \left({{1\over {m-2}}} \right)^2 \ $$