Question

Solve for ‘x’:
1/(2a+b+2x) = 1/2a +1/b+1/2x , x ≠ 0.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

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

1/(2a+b+2x) - 1/2x= 1/2a +1/b

(2x-2a-b-2x) / 2x(2a+b+2x) = 2a+b/2ab

-2a-b / 2x(2a+b+2x) = 2a+b/2ab

-(2a+b) / 2x(2a+b+2x) = 2a+b/2ab

-1/ x(2a+b+2x) = 1/ab

x(2a+b+2x) = - ab

2ax+xb+2x²+ab=0

2x²+2ax+bx+ab=0

2x(x+a)+ b( x+a)=0

(x+a) (2x+b)= 0

x+a=0,    (2x+b)= 0

x= -a ,      2x=-b, x= - b/2   

x= -a ,  -b/2

Hence , the value of x is x= -a ,  -b/2

HOPE THIS WILL HELP YOU....

Answer 2

Hey there,

1/(2a+b+2x) -1/2x=1/2a +1/2b

=>{2x-2a-b-2x}/2x(2a+b+2x)=(a+b)/2ab

=>(-2a-b)(2ab)=4ax+2bx+4x^2

=>4x^2+2(2a+b)x +2ab(2a+b)=0

use quadratic formula and solve it

Hope this helps!