Question

1. Check whether (x – 2)2 + 1= 2x – 3 is Q.E or not ?

Answer 1

Answer:

(x-2)2+1

=2x-4+1

=2x-3

Step-by-step explanation:

Hence Proved

Answer 2

Answer:

(x - 2)² + 1 = 2x - 3 is a quadratic equation.

Step-by-step explanation:

Question :

Check whether (x - 2)² + 1 = 2x - 3 is a quadratic equation or not ?

Solution :-

L.H.S :

⇒ (x - 2)² + 1

∵ (a - b)² = (a + b)(a - b)

⇒ (x)(x) + (x)(-2) + (-2)(x) + (-2)(-2) + 1

⇒ x² + (-2x) + (-2x) + (-4) + 1

⇒ x² + 4x + 4 + 1

⇒ x² - 4x + 5

∴,

⇒ x² - 4x + 5 = 2x - 3

⇒ x² - 4x - 2x + 5 = -3

⇒ x² - 6x + 8 = 0

Standard quadratic equation :-

➤ ax² + bx + c = 0

∵ x² - 6x + 8 = 0 = ax² + bx + c = 0

∴ It is a quadratic equation.

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Check whether the equation x(x + 1) + 8 = (x + 2)(x - 2) is quadratic equation or not ?