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PIT_PIT [208]
3 years ago
14

(x + 1)^2 = 3x – 1 solving Quadratics ?

Mathematics
2 answers:
Deffense [45]3 years ago
5 0

Step-by-step explanation:

(x + 1)^{2}  = 3x - 1 \\  \\  \therefore \:  {x }^{2}  + 2x + 1 = 3x - 1 \\  \\ \therefore \:  {x }^{2}  + 2x + 1  -  3x  + 1 = 0\\  \\ \therefore \:  {x }^{2}  + 2x  -  3x + 1 - 1 = 0 \\  \\ \therefore \:  {x }^{2}  - x  = 0 \\  \\ \therefore \:  x(x - 1) = 0 \\  \\ \therefore \: x = 0 \:  \: or \:  \: x - 1 = 0 \\  \\ \therefore \: x = 0 \:  \: or \:  \: x = 1 \\  \\  \huge{ \red{ \boxed{\therefore \: x =  \{0, \:  \: 1 \}}}}

FromTheMoon [43]3 years ago
4 0

Answer: x = - 1 or x = 2

Step-by-step explanation:

The given quadratic equation is expressed as

(x + 1)^2 = 3x – 1

Expanding the brackets, it becomes

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

x² + x + x + 1 = 3x - 1

x² + 2x - 3x + 1 + 1 = 0

x² - x + 2 = 0

We would find two numbers such that their sum or difference is -x and their product is 2x^2. The two numbers are x and 2x. Therefore,

x² + x - 2x + 2 = 0

x(x + 1) - 2(x + 1) = 0

(x + 1)(x - 2) = 0

x + 1 = 0 or x - 2 = 0

x = - 1 or x = 2

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