Question

1/x-3 - 1/x-8=11/30 find the value of x

Answer 1

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Answer 2

Answer:

The two values of the equations are

$x = \frac{121+5\sqrt{143}i}{22}$

$x = \frac{121-5\sqrt{143}i}{22}$

Step-by-step explanation:

As given the equation is written in the form .

$\frac{1}{x-3}-\frac{1}{x-8}=\frac{11}{30}$

Simplify the above equation

30×[(x-8)-(x-3)] = 11[ (x-3)(x-8)]

30× [x-x -8+3] = 11 × (x²-8x-3x+24)

30×[0-5] = 11 × (x² -11x + 24)

-150 = 11x² - 121x + 264

11x² - 121x + 264 + 150 = 0

11x² - 121x + 414 = 0  

Now by using the discriment formula

$x = \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

As the general form of the equation is

ax² + bx + c = 0

a = 11 , b = -121 , c = 414

Putting all the values in the formula

$x = \frac{-(-121)\pm\sqrt{121^{2}-4\times 11\times 414}}{2\times 11}$

$x = \frac{121\pm\sqrt{14641-18216}}{22}$

$x = \frac{121\pm\sqrt{-3575}}{22}$

$x = \frac{121\pm\sqrt{-3575}}{22}$

(As i = -1 )

$x = \frac{121+5\sqrt{143}i}{22}$

$x = \frac{121-5\sqrt{143}i}{22}$