Question

The equation (X-2)ᒾ +1 = 2X-3 is a_________.​

Answer 1

Quadratic equation
Hope it helps

Answer 2

SOLUTION

TO DETERMINE

The nature of the equation

$\sf{} {(x - 2)}^{2} + 1 = 2x - 3$

CONCEPT TO BE IMPLEMENTED

Any equation of the form

$\sf{}a {x}^{2} + bx + c = 0 \: \: \: , \: \: a \ne \: 0$

is a quadratic equation with respect to the variable x

EVALUATION

Here the given equation is

$\sf{} {(x - 2)}^{2} + 1 = 2x - 3$

Which can be simplified as below

$\sf{} {x}^{2} - 4x + 4 + 1 = 2x - 3$

$\implies \: \sf{} {x}^{2} - 4x + 5= 2x - 3$

$\implies \: \sf{} {x}^{2} - 6x + 8= 0$

This equation is of the form

$\sf{}a {x}^{2} + bx + c = 0 \: \: \: , \: \: a \ne \: 0$

Hence the given equation is a quadratic equation with respect to the variable x

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