Amit M Agarwal Solutions for Chapter: Inequalities and Quadratic Equation, Exercise 7: Entrances Gallery

The number of solution(s) of the equation $\sqrt{x+1}-\sqrt{x-1}=\sqrt{4x-1}$ is

If $9\sqrt{x}=\sqrt{12}+\sqrt{147},$ then the value of $x$ is

Solve the equation $x^2-\sqrt{3}x+1=0$

_{If $a=\cos \frac{2\pi }{7}+i\sin \frac{2\pi }{7},$ then the quadratic equation whose roots are $\alpha =a+a^2+a^4$ and $\beta =a^3+a^5+a^6,$}

Let $p$ and $q$ be real numbers. If $\alpha$ is the root of $x^2+3p^{2}x+5q^2=0, \beta$ is the root of $x^2+9p^{2}x+15q^2=0$ and $0<\alpha <\beta ,$ then the equation $x^2+6p^{2}x+10q^2=0$ has a root $\gamma$ that always satisfies

If the roots of the equation ${\lambda }^2+8\lambda +{\mu }^2+6\mu =0$ are real, then $\mu$ lies between

The number of solutions of the inequality $\left|x-2\right|+\left|x+2\right|<4$ is

Solve the inequality $2x-5\le \left(\frac{4x-7}{3}\right)$