MyQuestionIcon

1

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

Variable Separable Method

Solve the fol...

Question

Solve the following equation:
$\sqrt{3 x + 3} + \sqrt{3 x - 2} = 7$

Open in App

Solution

$\sqrt{3 x + 3} + \sqrt{3 x - 2} = 7$
squaring both sides -
$\Rightarrow 3 x + 3 + 3 x - 2 + 2 \sqrt{3 x + 3} \sqrt{3 x - 2} = 49$
$\Rightarrow 6 x + 1 + 2 \sqrt{3 x + 3} \sqrt{3 x - 2} = 49$
$\Rightarrow 2 \sqrt{3 x + 3} \sqrt{3 x - 2} = 48 - 6 x = 36 (8 - x)$
squaring both sides -
$\Rightarrow (3 x + 3) (3 x - 2) = 9 (64 + x^{2} - 16 x)$
$\Rightarrow 9 x^{2} + 9 x - 6 x - 6 = 9 x^{2} - 144 x + 576$
$\Rightarrow 3 x + 144 x = 576 + 6$
$\Rightarrow 147 x = 582$
$\Rightarrow x = \frac{194}{49}$
Hence, the answer is $\frac{194}{49} .$

Suggest Corrections

thumbs-up

1

Similar questions

Q. Solve the following equations:

3 x^{2} - 7 + 3 \sqrt{3 x^{2} - 16 x + 21} = 16 x

Q. Solve the following equation.

\frac{2}{3} x = \frac{3}{8} x + \frac{7}{12}

.

Q. Solve the following equation:

log (3 x^{2} + 7) - log (3 x - 2) = 1

Q. Solve the following equation:

\sqrt{2 x - 3} = \sqrt{7 - 3 x}

Q. Solve the following linear equation

\frac{7}{2} x + \frac{1}{2} x = 3 x + \frac{3}{2} + \frac{5}{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Methods of Solving First Order, First Degree Differential Equations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Variable Separable Method

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon