If a + a²+a³-1=0, then what is the value of a³ +(1/a)?

If x - y = 6 and xy = 40, then  find $$ {x^2+y^2}$$

If then the value of

If x = b+c -2a, y=c+a-2b, z=a+b-2c, then the value of x²+y²-z²+2xy is : 

If  $$\sqrt{a}+\sqrt{b}=15 \ and \ (\sqrt{a}-\sqrt{b} )=3$$ then the value of $$\sqrt{ab/4} $$ is 

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

Value of $$ \sqrt{6+\sqrt {6+\sqrt {6+....}}}$$

If x, y are two positive real number and  $$x^{1/3}=y^{1/4}$$, then which of the following relations is true?