If \(\left( { x }^{ \frac { 1 }{ 2 } }+{ x }^{ -\frac { 1 }{ 2 } } \right) ^{ 2 }=\frac { 9 }{ 2 } \), then find the value of \(\left( { x }^{ \frac { 1 }{ 2 } }-{ x }^{ -\frac { 1 }{ 2 } } \right) \)for x > 1

Prove that \(\sqrt { 3 } \) is an irrational number. (Hint: Follow the method that we have used to prove \(\sqrt { 2 } \notin Q\))

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number

Solve for x  \(\left| 3-\frac { 3 }{ 4 } x \right| \le \frac { 1 }{ 4 } \)

Solve log₈ x + log₄ x + log₂ x = 11

If a²+b² = 7ab. Show that log \(\ \frac { a+b }{ 3 } =\frac { 1 }{ 2 } \)  (log a + log b)

Determine the region in the Plane determined by the inequalities.
\(3x+5y\ge 45,\ x\ge 0,\ y\ge 0\)

Solve the equation \(\sqrt{6-4x-x^2}=x+4\)

Solve x = \(\sqrt{x+20}\) for x ∈ R

Shade the region given by the inequality x ≥ 2.