Question

$(x+1) ^{2} =2(x−3)$
Please solve this ​

Answer 1

Answer:

Answer :

The roots of the quadratic equation  (4/x) - 3 = 5/(2x + 3)  are 1 and - 2 .

Step-by-step explanation :

Given - (4/x) - 3 = 5/(2x + 3)  

⇒ [4 - 3x] /x  = 5/(2x + 3)  

By taking the LCM -

⇒ (4 - 3x) (2x + 3) = 5x

⇒ 8x +12 - 6x² - 9x = 5x  

⇒ -6x² + 8x - 9x - 5x +12 = 0

⇒ -6x² - 6x + 12 = 0

⇒ -6(x² + x - 2) = 0

⇒ x² + x - 2 = 0

⇒ x² + 2x  - x - 2 = 0

⇒ x(x + 2) - 1(x + 2) = 0

⇒ (x -1) (x + 2) = 0

⇒ x - 1 = 0 OR x + 2 = 0  

⇒ x = 1 OR x = -2

How to solve quadratic equations by factorization :

At first write the given quadratic polynomial as product of the two linear factors by splitting it's middle term.

Then equate both factor equivalent to zero to get the roots of given quadratic equation.