What is the one of the roots of the equation -2x3 - x - -3 - x2x - 32-

The correct option is B 2 √(2x3 x) √(3 x2x) = 32 (Let t = √(2x3 x)) ⇒ t 1t = 32⇒ 2t^2 3t 2 = 0⇒ (t 2)(2t+1) = 0 ⇒t = 2, 12⇒√(2x3 x) = ...

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

Byju's Answer

Standard XII

Mathematics

Discriminant

What is the o...

Question

What is the one of the roots of the equation $\sqrt{\frac{2 x}{3 - x}} - \sqrt{\frac{3 - x}{2 x}} = \frac{3}{2}$ ?

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2$
$\sqrt{\frac{2 x}{3 - x}} - \sqrt{\frac{3 - x}{2 x}} = \frac{3}{2}$ (Let $t = \sqrt{\frac{2 x}{3 - x}})$
$\Rightarrow t - \frac{1}{t} = \frac{3}{2} \Rightarrow 2 t^{2} - 3 t - 2 = 0 \Rightarrow (t - 2) (2 t + 1) = 0$
$\Rightarrow t = 2, - \frac{1}{2} \Rightarrow \sqrt{\frac{2 x}{3 - x}} = 2, \frac{- 1}{2} \Rightarrow \frac{2 x}{3 - x} = 4, \frac{1}{4}$
$\Rightarrow 2 x = 12 - 4 x \Rightarrow x = 2$ & $x = \frac{1}{3}$

Suggest Corrections

Similar questions

Q. Determine the sum of imaginary roots of the equation

(2 x^{2} + x - 1) (4 x^{2} + 2 x - 3) = 6

Q. The roots of the equation

2 x^{4} + x^{3} - 11 x^{2} + x + 2 = 0

is/are

Q. Rational roots of the equation

2 x^{4} + x^{3} - 11 x^{2} + x + 2 = 0

are

Q. Find the equation whose roots are the squares of the roots of

x^{4} + x^{3} + 2 x^{2} + x + 1 = 0

The roots of the quadratic equation $x^{2} - 2 x - 3 = 0$ are $- 1$ and $3$ . The graph of $x^{2} - 2 x - 3$ will pass through which of the following points.

Join BYJU'S Learning Program

What is the one of the roots of the equation √2x3−x−√3−x2x=32?

The correct option is B 2√2x3−x−√3−x2x=32 (Let t=√2x3−x)⇒t−1t=32⇒2t2−3t−2=0⇒(t−2)(2t+1)=0⇒t=2,−12⇒√2x3−x=2,−12⇒2x3−x=4,14⇒2x=12−4x⇒x=2 & x=13

What is the one of the roots of the equation $\sqrt{\frac{2 x}{3 - x}} - \sqrt{\frac{3 - x}{2 x}} = \frac{3}{2}$ ?