Question

if (2x+1)!×(x-1)!/(x+2)!×(2x-1)!=3/5 ;find x​

Answer 1

Step-by-step explanation:

we know,

$f(2x + 1) =( 2x + 1) \times 2x \times f(2x -1 )$

so

$f(x + 2) = (x + 2) \times (x + 1) \times x \times f(x)$

here

$f(x) = \: factorial \: of \: x$

so the equation simplifies to be

$\frac{(2x + 1) \times 2x}{(x + 2) \times (x + 1) \times x} = \frac{3}{5}$

this simplifies to be

$\frac{4x + 2}{ {x}^{2} + 3x + 2 } = \frac{3}{5}$

or

$20x + 10 = 3 {x}^{2} + 9x + 6$

or

$3 {x}^{2} - 11x - 4 = 0$

or

$3 {x}^{2} - 12x + x - 4 = 0$

or

$3x(x - 4) + 1(x - 4) = 0$

or

$(3x + 1)(x - 4) = 0$

or

$x = - \frac{1}{3}$

and

$x = 4$

since the factorial of negative numbers does not exist so we can say that

x should be equal to 4

hope this helps you. please mark my answer as the brainliest.