CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Terms

Solve 1x+a+...

Question

Solve $\frac{1}{x + a} + \frac{1}{x + 2 a} + \frac{1}{x + 3 a} = \frac{3}{x}$

Open in App

Solution

$\frac{1}{x + a} + \frac{1}{x + 2 a} + \frac{1}{x + 3 a} = \frac{3}{x}$
$(x + 2 a) (x + 3 a) + (x + a) (x + 3 a) + (x + a) (x + 2 a) = \frac{3}{x} (x + a) (x + 2 a) (x + 3 a)$
$x^{2} + 5 a x + 6 x^{2} + x^{2} + 4 a x + 3 a^{2} + x^{2} + 3 x a + 2 a^{2} = \frac{3}{x} [(x^{2} + 3 x a + 2 a^{2}) (x + 3 a)]$
$3 x^{2} + 12 a x + 11 a^{2} = \frac{3}{x} (x^{3} + 3 x^{2} a + 2 x a^{2} + 3 a x^{2} + 9 x a^{2} + 6 a^{3})$
$3 x^{2} + 12 a x^{2} + 11 a^{2} x = 3 x^{2} + 18 x^{3} a + 33 x a^{2} + 18 a^{2}$
$6 x^{2} a + 22 a^{2} x + 18 a^{3} = 0$
$\Rightarrow 3 x^{2} a + 11 a x + 9 a^{2} = 0$
$x = \frac{- 11 a \pm \sqrt{121 a^{2} - 108 a^{2}}}{6} = \frac{- 11 \pm 9 \sqrt{13}}{6}$

Suggest Corrections

thumbs-up

0

Similar questions

(x^{5} + 1), (3 - x^{4}), (4 + x^{3} + x^{6})

-

(2 a^{3} - 3 b^{5}), (2 a^{3} + 3 b^{5}), (2 a^{4} - 3 a^{2} b^{2} + b^{4})

(1 - a^{2}) (x + a) - 2 a (1 - x^{2}) = 0

Q. Solve the equation

x + \frac{3}{2} = \frac{5}{2}

Q. If the sum of zeroes of p(x)=(a+1)

x^{2}

+(2a+3)x+(3a+4) is -1.Find its product.

Q. Find whether the following series are convergent or divergent:

\frac{1}{x} - \frac{1}{x + a} + \frac{1}{x + 2 a} - \frac{1}{x + 3 a} + . . . ., x

a

being positive quantities.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon