Question

19. Solve : 2x–3/x=1 ​

Answer 1

Answer:

2x-3/x=1

(2x^2-3)/x=1

2x^2-3=x

2x^2-x-3=0

x=(-b+ or -√b^2-4ac)/2a

here a=2, b=-1, c=-3

b^2-4ac=-1^2-4×2×-3

=1-8×-3

=1+24

=25

√b^2-4ac=√25

=5

-b+or-(√b^2+4ac)/2a

=(1+or-5)/2×2

=(1+5)/4

=6/4

=3/2

or

(1-5)/2×2

=(1-5)/4

=-4/4

=-1

Taking positive number

hence x=3/2

you can verify the answer by

giving the value of ×=3/2 in 2x-3/x=1

2×3/2-3/(3/2)

=3-3×2/3

=3-2

=1☺️☺️☺️☺️

Answer 2

Answer:

2x - 3/x = 1

2x² - 3 / x = 1

2x² - 3 = x

2x² - x - 3

Now, Factorising 2x² - x - 3 =

2x² + 2x - 3x - 3

2x(x+1)-3(x+1)

(2x-3)(x+1)

Factors are -

2x - 3 = 0

2x = 3

x = 3/2

And

x + 1 = 0

x = - 1