List of top Mathematics Questions on Inequalities

Find the value of 'n' so that \( \frac{a^{n+1} + b^{n+1}}{a^n + b^n} \) may be the geometric mean between a and b.

Solve the given inequality for real \( x \): \[ \frac{3(x - 2)}{5} \leq \frac{5(2 - x)}{3} \]

Solve the given inequalities and represent the solution graphically on the number line: \[ 2(x - 1)<x + 5, \quad 3(x + 2)>2 - x \]

The equation of a line in the intercept form is:

Prove that for any two non-zero vectors \( \mathbf{a} \) and \( \mathbf{b} \), \[ |\mathbf{a} + \mathbf{b}| \leq |\mathbf{a}| + |\mathbf{b}| \] Also, write the name of this inequality.

Name of the inequality \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) is:

Which values of x are satisfied by the inequality 2x² + x-3 <0?

If x is a positive number, then which of the following fractions has the greatest value?