Question

Q.Find the roots of the equation:
1/(2x−3)+1/(x−5)=1, x ≠ 3/2, 5.

please answer fast!!!​

Answer 1

Answer:

Main concept used: For real roots of quadratic equationax2+bx+c=0,b2−4ac>0

(iv) (2x−3)1+(x−5)1=1,x=23,5

(2x−3)1+(x−5)1=1,x=23,5

⇒(2x−3)(x−5)(x−5)+(2x−3)=1

⇒x−5+2x−3=2x2−3x−10x+15

⇒2x2−13x+15=3x−8

⇒2x2−13x+15−3x+8=0

⇒2x2−16x+23=0

Now, D=b