Question

solve the quadratic equation by factorisation
a+1/2a-3=a+5/a+3
​

Answer 1

Answer:

a + 1/2a - 3 = a + 5/a + 3

cross multiple

( a + 1)(a + 3) = (a + 5)(2a - 3)

a² + 3a + a + 3 = 2a² - 3a + 10a - 15

a² + 4a + 3 = 2a² + 7a - 15

2a² - a² + 7a - 4a - 15 - 3 = 0

a² + 3a - 18 = 0

Answer 2

Answer :

a = 3 (or) -6

Step-by-step explanation :

$\sf \frac{a+1}{2a-3} =\frac{a+5}{a+3} \\\\ (a+1)(a+3)=(a+5)(2a-3) \\\\ a(a+3)+1(a+3)=a(2a-3)+5(2a-3) \\\\ a^2+3a+a+3=2a^2-3a+10a-15 \\\\ a^2+4a+3=2a^2+7a-15 \\\\ 2a^2-a^2+7a-4a-15-3 =0 \\\\ a^2+3a-18=0$

The quadratic equation we got is

a² + 3a - 18 = 0

Steps to factorize :

Quadratic term = a²

Linear term = 3a

Constant term = -18

>> Find the product of quadratic term and constant term

 = a² × (-18)

 = -18a²

>> Find the factors of "-18a²" in pairs

  (a) (-18a)

  (-18a) (a)

  (2a) (-9a)

  (-2a) (9a)

  (3a) (-6a)

  (-3a) (6a)

>> From the above, find the pair that adds to get linear term

  6a - 3a = 3a

>> Split 3a as 6a and 3a

  a² + 3a - 18 = 0

  a² + 6a - 3a - 18 = 0

>> Find the common factor,

  a(a + 6) - 3(a + 6) = 0

  (a + 6) (a - 3) = 0

=> a + 6 = 0 ; a = -6

=> a - 3 = 0 ; a = +3