Question

solve the following quadratic equation

Answer 1

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 gets cancelled.

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

-2ab = 4ax + 2bx + 4x2

4x2 + 2bx + 4ax + 2ab = 0

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

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

2x + 2a = 0

x = - a

2x + b = 0

x = - b / 2

Ans: x = -a , -b/2



.

2/(x+1) +3/2(x−2)=23/5x
⇒4(x−2)+3(x+1)/2(x+1)(x−2)=23/5x
⇒{4x−8+3x+3}/2(x2−2x+x−2)=23/5x
⇒5x(7x−5)=46(x2−x−2)
⇒35x2−25x=46x2−46x−92
⇒11x2−21x−92=0
⇒x=[21±root{(−21)2−4×11×(−92)}]/2×11
⇒x=[21±√(4489)]/22
⇒x=(21±67)/22
⇒x=88/22 or x=−46/22⇒x=4 or x=−23/11