Question

(x-2)^2+1=2x-3 check whether quadratic equations or not​

Answer 1

(x-2)^2+1=2x-3

{a-b}^2=a^2+b^2-2ab

x^2+2^2-2(x)(2)+1-2x+3=0

x^2+4-4x+1-2x+3=0

x^2-6x+8

hence its a quadaratic equation

Answer 2

Given,

Equation:

(x - 2)² + 1 = 2x - 3

To find,

Check whether the given equation is quadratic.

Solution,

Here, the given equation is,

(x - 2)² + 1 = 2x - 3

A quadratic equation is a polynomial or an algebraic expression with one variable and having the degree 2. Quadratic equations are of the form,

$ax^2+bx+c=0$

Where x is the variable and the unknown,

a, b, c are known numbers, and a ≠ 0.

Now, simplifying the given equation that is,

(x - 2)² + 1 = 2x - 3

(x² - 2·(x)·(2) + 2²) + 1 = 2x - 3

x² - 4x + 4 + 1 = 2x - 3

x² - 4x - 2x + 5 + 3 = 0

x² - 6x + 8 = 0

On comparing, it can be seen that the obtained equation is of the form

$ax^2+bx+c=0$, having degree 2 of the variable x.

Therefore, the given expression (x - 2)² + 1 = 2x - 3, is a quadratic equation.