Question

EXERCISE - 5.1
Check whether the following are quadratic equations :
i. (x + 1)2 = 2(x – 3)
ii. x² – 2x = (-2) (3 – x)

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Answer 1

Answer:

$(x + 1) 2 = 2(x - 3) \\ \\ x2 + 1 + 2x = 2x - 6 \\ \\ x2 + 1 + 2x - 2x + 6 = 0 \\ \\ x2 + 7 = 0 \\ \\ given \: equation \: is \: quadratic \: equation.$

given equation is quadratic equation.

$x2 - 2x = ( - 2)(3 - x). \\ \\ x2 - 2x = - 6 + 2x \\ \\ x2 - 2x - 2x + 6 = 0 \\ \\ x2 - 4x + 6 = 0. \\ \\ it \: is \: a \: quadratic \: equation$

my answer is correct.

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Answer 2

$\sf\large\pink{\underline{\underline{ \: Question\:1 \: }}}$

Given:

• (x + 1)² = 2(x – 3)

Solution:

By using the formula for (a+b)² = a²+2ab+b²

⇒ x² + 2x + 1 = 2x – 6

⇒ x² + 7 = 0

Since the above equation is in the form of ax² + bx + c = 0.

Therefore, the given equation is quadratic equation.

$\\ \sf\large\pink{\underline{\underline{ \: Question\:2 \: }}}$

Given:

x² – 2x = (–2) (3 – x)

By using the formula for (a+b)² = a²+2ab+b²

⇒ x² – 2x = -6 + 2x

⇒ x² – 4x + 6 = 0

Since the above equation is in the form of ax² + bx + c = 0.

Therefore, the given equation is quadratic equation.