MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Linear Equation in One Variable

Solve the fol...

Question

Solve the following equations:
$\sqrt{2 x^{2} - 9 x + 4} + 3 \sqrt{2 x - 1} = \sqrt{2 x^{2} + 21 x - 11}$ .

Open in App

Solution

$\sqrt{2 x^{2} - 9 x + 4} + 3 \sqrt{2 x - 1} = \sqrt{2 x^{2} + 21 x - 11} \sqrt{2 x^{2} - 9 x + 4} + 3 \sqrt{2 x - 1} - \sqrt{2 x^{2} + 21 x - 11} = 0 \sqrt{2 x^{2} - 8 x - x + 4} + 3 \sqrt{2 x - 1} - \sqrt{2 x^{2} - x + 22 x - 11} = 0 \sqrt{2 x (x - 4) - 1 (x - 4)} + 3 \sqrt{2 x - 1} - \sqrt{x (2 x - 1) + 11 (2 x - 1)} = 0 \sqrt{(2 x - 1) (x - 4)} + 3 \sqrt{2 x - 1} - \sqrt{(x + 11) (2 x - 1)} = 0 \sqrt{2 x - 1} (\sqrt{x - 4} + 3 - \sqrt{x + 11)}) = 0$
$\Rightarrow \sqrt{2 x - 1} = 0$ $\Rightarrow x = \frac{1}{2}$
and $\sqrt{x - 4} + 3 - \sqrt{x + 11} = 0$
$\sqrt{x - 4} + 3 - \sqrt{x + 11} = 0 \sqrt{x - 4} + 3 = \sqrt{x + 11}$
Squaring both sides
$x - 4 + 9 + 6 \sqrt{x + 4} = x + 11 6 \sqrt{x - 4} = 6 \sqrt{x - 4} = 1$
Again squaring both sides
$x - 4 = 1 x = 5$
So the values of $x$ are $\frac{1}{2}$ and $5$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Solve the following equations:

\sqrt{2 x^{2} - 7 x + 1} - \sqrt{2 x^{2} - 9 x + 4} = 1

Q. Solve the following equation:

\sqrt{x^{2} + x + 4} + \sqrt{x^{2} + x + 1} = \sqrt{2 x^{2} + 2 x + 9}

Q. Solve the following inequality:

\frac{1 + 3 x^{2}}{2 x^{2} - 21 x + 40} < 0

Q. The values of

x

which satisfy the equation

\sqrt{{5 x}^{2} - 8 x + 3} - \sqrt{{5 x}^{2} - 9 x + 4} = \sqrt{({2 x}^{2} - 2 x)} - \sqrt{({2 x}^{2} - 3 x + 1)}

Q. Solve the following quadratic equation,

2 (x^{2} + \frac{1}{x^{2}}) - 9 (x - \frac{1}{x}) + 14 = 0

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Framing a Linear Equation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Linear Equation in One Variable

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon