Question

Check whether the following are quadratic equations
(a) (x-2)²+1=2x-3

Answer 1

(x-2)^2+1=2x-3
x^2-4x+4+1=2x-3
x^2-4x+5=2x-3
x^2-6x+8=0
Solving by factorization:
Sum= -6
Product= 8
Factors= -4, -2
Therefore, (x-4)(x-2)
x=4,2

Answer 2

Sᴏʟᴜᴛɪᴏɴ:

LHS = (x - 2)² + 1

= x² - 4x + 4 + 1

= x ² - 4x + 5

Therefore, (x - 2)² + 1 = 2x - 3 can be written as x² - 4x + 5 = 2x - 3

i.e., x² - 6x + 8 = 0

It is in the form of ax² + bx + c = 0. Therefore, the given equation is a quadratic equation