Question

Solve the following quadratic equations by factorization: $\frac{1}{2a+b+2x}= \frac{1}{2a}+\frac{1}{b}+ \frac{1}{2x}$

Answer 1

SOLUTION :  

Given : 1/(2a + b + 2x) = 1/2a + 1/b + 1/2x

1/(2a + b + 2x) - 1/2a = 1/2x + 1/b  

[2a - (2a + b + 2x) / [(2a + b + 2x) (2a)]  = [(b + 2x)/2bx]  

[By taking LCM]

[2a - 2a - b - 2x / [(4a² + 2ab + 4ax)]  = [(b + 2x)/2bx]  

[- b - 2x] / [(4a² + 2ab + 4ax)]  = [(b + 2x)/2bx]  

- 1 (2x + b) / [(4a² + 2ab + 4ax)]  = [(b + 2x)/2bx]  

- 1 (2x + b) × 2bx = (4a² + 2ab + 4ax) (b + 2x)

(4a² + 2ab + 4ax) (b + 2x) + (2x + b) × 2bx = 0

(2x + b) [ (4a² + 2ab + 4ax) + 2bx] = 0

(2x + b) = 0  or  [(4a² + 2ab + 4ax + 2bx] = 0

2x = - b  or  4a² + 2ab + (4a + 2b)x = 0

x = - b/2  or   (4a + 2b)x = - a(4a + 2b)

x = - b/2  or   x = - a(4a + 2b)/(4a + 2b)

x = - b/2  or   x = - a  

Hence, the roots of the quadratic equation 1/(2a + b + 2x) = 1/2a + 1/b + 1/2x  are - b/2  & - a.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

i give u an example...