Using componendo and dividendo find out the value of x- -3 x-4-3 x-5-3 x-4-3 x-5-9A- 5B- 3C- 7D- 9

The correct option is C 7 ⇒( √(3x+4)+ √(3x 5))+(√(3x+4) √(3x 5))/(√(3x+4)+ √(3x 5)) (√(3x+4) √(3x 5)) = 9+1/9 1 ⇒2 √(3x+4)/2 √(3x 5)= 10/8= 5/4 ⇒ Si ...

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Standard X

Mathematics

Componendo and Dividendo

Using compone...

Question

Using componendo and dividendo find out the value of x.
$\frac{\sqrt{3 x + 4} + \sqrt{3 x - 5}}{\sqrt{3 x + 4} - \sqrt{3 x - 5}} = 9$

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Solution

The correct option is C
7

$\Rightarrow \frac{(\sqrt{3 x + 4} + \sqrt{3 x - 5}) + (\sqrt{3 x + 4} - \sqrt{3 x - 5})}{(\sqrt{3 x + 4} + \sqrt{3 x - 5}) - (\sqrt{3 x + 4} - \sqrt{3 x - 5})} = \frac{9 + 1}{9 - 1} \Rightarrow \frac{2 \sqrt{3 x + 4}}{2 \sqrt{3 x - 5}} = \frac{10}{8} = \frac{5}{4}$
$\Rightarrow$ Simplyfying and squaring both sides
$\frac{3 x + 4}{3 x - 5} = \frac{25}{16} 48 x + 64 = 75 x - 125 64 + 125 = 75 x - 48 x 189 = 27 x x = 7$

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Similar questions

Q. Using componendo and dividendo, find the value of

x

\frac{\sqrt{3 x + 4} + \sqrt{3 x - 5}}{\sqrt{3 x + 4} - \sqrt{3 x - 5}} = 9

Q. Using properties of proportion solve:

\frac{\sqrt{3 x + 4} + \sqrt{3 x - 4}}{\sqrt{3 x + 4} - \sqrt{3 x - 5}} = 9

Find the value of $x$ .

$3 x + \frac{9}{3} = 5 x + \frac{5}{9}$

Find the number of values of x satisfying

$3 x - 3 \leq 7 x + 5 a n d 5 - x \geq (\frac{x}{4}) - (\frac{5}{4}), w h e r e x ϵ N .$

Find the value of x.

$3 x + \frac{9}{3} = 5 x + \frac{5}{9}$

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Using componendo and dividendo find out the value of x. √3x+4+√3x−5√3x+4−√3x−5=9

The correct option is C 7 ⇒(√3x+4+√3x−5)+(√3x+4−√3x−5)(√3x+4+√3x−5)−(√3x+4−√3x−5) =9+19−1⇒2√3x+42√3x−5=108=54 ⇒ Simplyfying and squaring both sides 3x+43x−5=251648x+64=75x−12564+125=75x−48x189=27xx=7

Using componendo and dividendo find out the value of x.
$\frac{\sqrt{3 x + 4} + \sqrt{3 x - 5}}{\sqrt{3 x + 4} - \sqrt{3 x - 5}} = 9$