Discussion of Questions on Algebra

If x = $5 + 2√6$, then $√x + 1/√x$= ?

If x = $√3 + √2$, then $x^3 + 1/{x^3}$ = ?

If $4b^2 + 1/{b^2} = 2$, then $8b^3 + 1/{b^3} = ?$

$a/b + b/a = 1$, then $a^3 + b^3 = ?$

$(x + 1/x)(x - 1/x)(x^2 + 1/{x^2} - 1)(x^2 + 1/{x^2} + 1) = ?$

If $2x + 1/x = 4$, then $x^3 + 1/{8x^3} = ?$

If $xy(x + y) = 1$, then $1/{x^3y^3} - x^3 - y ^3 = ?$

If $m + 1/{m - 2} = 4$, then $(m - 2)^2 + 1/(m - 2)^2 = ?$

If $x^2 - 3x + 1 = 0$, then $x^3 + 1/{x^3} = ?$

If $x - 1/x = 4$, then $x + 1/x = ?$

If $x + 1/x = √3$, then $x^18 + x^12 + x ^6 + 1 = ?$

If $x = p + 1/p$ and $y = p - 1/p$, then $x^4 - 2x^2y^2 + y^4 = ?$

If $x = p + 1/p$ and $y = p - 1/p$, then $x^4 - 2x^2y^2 + y^4 = ?$

If $x + 1/x = 1$, then ${x^2 + 3x + 1}/{x^2 + 7x + 1} = ?$

If $x + 1/x = 2$, then $x^2013 + 1/x^2014 = ?$

If $x^{1/3} + y^{1/3} - z^{1/3} = 0$, then $(x + y + z)^3 + 27xyz = ?$

If $a + b + c = 0$, then ${a^2 + b^2 + c^2}/{a^2 - bc}$ = ?

If $x^2 = y + z, y^2 = z + x, z^2 = x + y$, then what is the value of $1/{x + 1} + 1/{y + 1} + 1/{z + 1}$?

If $a = √{7 + 2√12}$ and $b = √{7 - 2√12}$, then $a^3 + b^3 = ?$

If $x^2 + y^2 + 2y + 4x + 5 = 0$, then what is $x - 2y ?$

If $x/{1 - x} + y/{1 - y} + z/{1 - z} = 1$, then, what is $1/{1 - x} + 1/{1 - y} + 1/{1 - z}$ ?

If $a + b = 4$, and $1/a + 1/b = 4$, then the value of $a^3 + b^3 = ?$

If $m + 1/n = 1$ and $n + 1/p = 1$, then what is $p + 1/m ?$

If $p/{2p^2 + 5p + 2} = 1/6$, then $(p + 1/p) = ?$

Simplify $√{1 + ({x^4 - 1}/{-2x^2})^2}$ ?

If $x = 5/18$, then what is the value of $27x^3 - 1/216 - {9/2}x^2 + {1/4}x$ ?

If x = 11, then $x^5 - 12x^4 + 12x^3 - 12x^2 + 12x - 1$ is ?

The value of $1/{a^2 + ax + x^2} - 1/{a^2 - ax + x^2} + {2ax}/{a^4 + a^2x^2 + x^4}$ is ?