The equation ${\left(\frac{x}{x+1}\right)}^2+{\left(\frac{x}{x-1}\right)}^2=a\left(a-1\right)$ has

Important Questions on Theory of Equations

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 37

If the quadratic equations, $x^2+bx+c=0$ and $b{x}^2+cx+1=0$ have a common root then

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 38

If the inequality ${\cot }^{2}x+\left(k+1\right)\cot x-\left(k-3\right)<0$ is true for at least one $x\in \left(0,\frac{\mathrm{\pi }}{2}\right)$, then $k\in$

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 1

If $x=2+2^{\frac{2}{3}}+2^{\frac{1}{3}}$ then the value of $x^3-6x^2+6x$ is                      .

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 2

If $\sqrt{\sqrt{\sqrt{x}}}=\sqrt[4]{\sqrt[4]{\sqrt[4]{3x^4+4}}},$ then the value of $x^4$ is                               .

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 3

Sum of the values of $x$ satisfying the equation $\sqrt{2x+\sqrt{2x+4}}=4$ is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 4

If $a^2-4a+1=4,$ then the value of $\frac{a^3-a^2+a-1}{a^2-1} \left(a^2\ne 1\right)$ is equal to                 .

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 5

If $a$ and $b$ are positive numbers and each of the equations $x^2+ax+2b=0$ and $x^2+2bx+a=0$ has real roots, then the smallest possible value of $\left(a+b\right)$ is                   .

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 6

Given that $x^2-3x+1=0$, then the value of the expression $y =x^9+x^7+x^{-9}+x^{-7}$ is              .