Question

Find the roots of the following equation
1/x+3 - 1/x-8=11/33;x is not equal to -3,8

Answer 1

Answer:  Let

    x = 1

So,    $\frac{1}{1}$ + 3 -$\frac{1}{1}$ - 8 = $\frac{11}{33}$

∴ Hence,  1 = 1  

Answer 2

Answer:

The roots of the equations are $x = \frac{5+ \sqrt{11}i}{2}$ and $x = \frac{5-\sqrt{11}i}{2}$ .

Step-by-step explanation:

As given the expression in the equation is as follow .

$\frac{1}{x+3} - \frac{1}{x-8} = \frac{11}{33}$

Simplify the above

3 × (x - 8 - x - 3) = (x + 3) × (x - 8)

3 × (-11) = (x + 3) × (x - 8)

-33= x² -8x + 3x - 24

x² - 5x -24 + 33 = 0

x² - 5x + 9 = 0

As the equation is general form of the equation is

ax² + bx + c = 0

a = 1 , b = -5 , c = 9

Now by using the discriment formula

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

$x = \frac{-(-5) \pm\sqrt{(-5)^{2}-4\times 1\times 9}}{2\times 1}$

$x = \frac{5\pm\sqrt{25-36}}{2}$

$x = \frac{5\pm\sqrt{-11}}{2}$

As

√-1 = i

Thus

$x = \frac{5+ \sqrt{11}i}{2}$

$x = \frac{5-\sqrt{11}i}{2}$

Therefore the roots of the equations are $x = \frac{5+ \sqrt{11}i}{2}$ and $x = \frac{5-\sqrt{11}i}{2}$ .