Question

check wheather the following is quadratic (x-2)(x+1)=(x-1)(x+3)​

Answer 1

Answer:

Hello mate ✌️..

Step-by-step explanation:

) (x + 2)2 = 2(x - 3)

⇒ x2 + 2x + 1 = 2x - 6

⇒ x2 + 7 = 0

It is of the form ax2 + bx + c = 0.

Hence, the given equation is quadratic equation.

(ii) x2 - 2x = (-2)(3 - x)

⇒ x2 - 2x = -6 + 2x 

⇒ x2 - 4x + 6 = 0

It is of the form ax2 + bx + c = 0.

Hence, the given equation is quadratic equation.

(iii) (x - 2)(x + 1) = (x - 1)(x + 3)

⇒ x2 - x - 2 = x2 + 2x - 3

⇒ 3x - 1 =0

It is not of the form ax2 + bx + c = 0.

Hence, the given equation is not a quadratic equation.

(iv) (x - 3)(2x + 1) = x(x + 5)

⇒ 2x2 - 5x - 3 = x2 + 5x

⇒  x2 - 10x - 3 = 0

It is of the form ax2 + bx + c = 0.

Hence, the given equation is quadratic equation.

(v) (2x - 1)(x - 3) = (x + 5)(x - 1)

⇒ 2x2 - 7x + 3 = x2 + 4x - 5

⇒ x2 - 11x + 8 = 0

It is of the form ax2 + bx + c = 0.

Hence, the given equation is quadratic equation.

(vi) x2 + 3x + 1 = (x - 2)2

⇒ x2 + 3x + 1 = x2 + 4 - 4x

⇒ 7x - 3 = 0

It is not of the form ax2 + bx + c = 0.

Hence, the given equation is not a quadratic equation.

(vii) (x + 2)3 = 2x(x2 - 1)

⇒ x3 + 8 + x2 + 12x = 2x3 - 2x

⇒ x3 + 14x - 6x2 - 8 = 0

It is not of the form ax2 + bx + c = 0.

Hence, the given equation is not a quadratic equation.

(viii) x3 - 4x2 - x + 1 = (x - 2)3

⇒  x3 - 4x2 - x + 1 = x3 - 8 - 6x2  + 12x

⇒ 2x2 - 13x + 9 = 0

It is of the form ax2 + bx + c = 0.

Hence, the given equation is quadrati equation

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Answer 2

Answer:

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

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