Embibe Experts Solutions for Chapter: Algebraic Expressions, Exercise 1: Exercise 1

If $x^4+\frac{1}{x^4}=3842$, then the positive value of $x+\frac{1}{x}$ will be ______.

If ${\left(4x-5\right)}^3+{(x-2)}^3+27{(2x-5)}^3=9(4x-5)(x-2)(2x-5)$, then the value of $\left(x+\frac{3}{2}\right)$ will be:

If $x^4-12x^2+1=0$, then what will be the value of $x^4+\frac{1}{x^4}?$

If $\left(x^2+\frac{1}{49x^2}\right)=15\frac{5}{7}$, then what is the value of $\left(x+\frac{1}{7x}\right)$?

If $a+b+c=2 \text{and} ab+bc+ca=-1,$ then the value of $a^3+b^3+c^3-3abc$ is:

The last two digits of ${37}^2$ is.

If $9x^2-6x+1=0$, then the value of $27x^3+{\left(27x^3\right)}^{-1}$ will be:

If $x+\frac{81}{x}=18$ where $x>0$, then the value of $x^2+\frac{162}{x^2}$ is: