Question

If the following equation is true that is $5+2\sqrt{3}=\alpha -6\sqrt{3}$ then find the value of $\alpha $.

Answer 1

Hint: First we will define what an algebraic equation is and then we will define its types. After that, we will take the given equation in the question and solve it. Therefore, we will find the value of the unknown variable that is $\alpha $ and hence finally get the answer.

Complete step by step answer:
We are given an algebraic equation and asked to solve for a variable, so for that, we will first define what are algebraic equations. An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. In simple words, equations mean equality that is the equal sign. That’s what equations are all about- “equating one quantity with another”.
Now, we will see the types of algebraic equations.
A. Polynomial Equations: All the polynomial equations are a part of algebraic equations like the linear equations. So, a polynomial equation is an equation consisting of variables, exponents and coefficients. Linear equations are of the form: $ax+b=c$ where, $a\ne 0$
B. Quadratic Equations: A quadratic equation is a polynomial equation of degree $2$ in one variable of type $f\left( x \right)=a{{x}^{2}}+bx+c$
C. Cubic Equations: The cubic polynomials are polynomials with degree $3$. All the cubic polynomials are also algebraic equations. They are of the type: $a{{x}^{3}}+b{{x}^{2}}+cx+d=0$
We are given $5+2\sqrt{3}=\alpha -6\sqrt{3}$, now we will move \[6\sqrt{3}\] from the right hand side to the left hand side, thus we will get: $5+2\sqrt{3}+6\sqrt{3}=\alpha $ , finally we will add common terms and get the value of $\alpha $ :
Therefore, the answer is $\alpha =5+8\sqrt{3}$

Note:
Sometimes students can get confused between the expressions and equations. Expressions are true for all values of $x$ and the common key terms for expression are: simplify, expand and factorize, for example, $8x+5y-3x-5$ whereas equations are true for some values of $x$ and the common key terms for an equation is solved, for example, $5x-4=x$ .