Question

Which of the following is a quadratic equation?

1️⃣ (x - 2)(x + 1) = (x - 1)(x + 3)
2️⃣ x² + 3x + 1 = (x - 2)²
3️⃣ (x + 1)² = 2(x - 3)
4️⃣ (x + 2)³ = 2x(x² - 1)​

Answer 1

Answer:

1.)(x-2)(X+1) = (x-1)(X+3)

x²+x-2x-2=x²+3x-x-3

x²-x-2=x²+2x-3

x²-x²+2x+x-3+2

x-1

here degree iis not two so it's not an q.e

2.)x²+3x+1= (x-2)²

x²+3x+1= x²-4x+4

x²-x²+3x+4x+1-4

7x-3

here degree is 1 so it's not q.e

3.)X+1)²=2(x-3)

x²+2x+1=2x-6

x²+2x-2x+1+6

x²+7

here degree is two so it's a q.e

4.)(X+2)³=2x(x²-1)

x³+3x²(2)+3x(2)²+2³=2x³-2x

x³+6x²+12x²+8=2x³-2x

x³+18x²+8=2x³-2x

2x³-x³-18x²-2x-8

x³-18x³-2x-8

hense it's degree is 3 it's not a q.e

therefore option 3 is a q.e(quadratic equation)

Answer 2

Given :

1️⃣ (x - 2)(x + 1) = (x - 1)(x + 3)

2️⃣ x² + 3x + 1 = (x - 2)²

3️⃣ (x + 1)² = 2(x - 3)

4️⃣ (x + 2)³ = 2x(x² - 1)​

To Find :  a quadratic equation

Solution:

quadratic equation

ax² + bx + c = 0

where a ≠ 0

(x - 2)(x + 1) = (x - 1)(x + 3)

=> x²  - x - 2  = x²  + 2x - 3

=> x  + 1 = 0

linear Equation

x² + 3x + 1 = (x - 2)²

=> x² + 3x + 1 = x²  - 4x + 4

=> 7x  = 3

Linear equation

(x + 1)² = 2(x - 3)

=> x²  + 2x + 1 = 2x - 6

=> x²  + 7 = 0

Hence Quadratic Equation

(x + 2)³ = 2x(x² - 1)​

x³ + 6x² + 12x + 8  = 2x³  - 2x

=> x³  - 6x² - 14x - 8 = 0

cubic Equation

Hence (x + 1)² = 2(x - 3) is correct answer

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