Question

EXERCISE 4.1
Check whether the following are quadratic equations
(¡)(x+1)²=2(x-3)
(¡¡)x²-2x=(-2)(3-x)
(¡¡¡)(x-2)(x+1)=(x-1)(x+3)
(¡v)(x-3)(2x+1)=x(x+5)​

Answer 1

Answer:

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

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

$(x - 2)(x + 1) = (x - 1)(x + 3) \\ \\ x2 + x - 2x - 2 = x2 + 3x - x - 3 \\ \\ x2 - x - 2 = x2 + 2x - 3 \\ \\ - x - 2 = - 2x + 3 \\ \\ it \: is \: not \: quadratic \: equation$

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