Question

can any one solve this​

Answer 1

HOPE THIS IS HELPFUL...

Answer 2

Answer:

3. x=7. And 4. Answer is 2

Step-by-step explanation:

3.

$\frac{ \sqrt{3x + 4} + \sqrt{3x - 5} }{ \sqrt{3x + 4} - \sqrt{3x - 5} } = 9</p><p> \\ </p><p>\frac{(\sqrt{3x + 4} + \sqrt{3x - 5}) + (\sqrt{3x + 4} - \sqrt{3x - 5})}{ (\sqrt{3x + 4} + \sqrt{3x - 5}) - (\sqrt{3x + 4} - \sqrt{3x - 5}) } = \frac{9 + 1}{9 - 1} \\ \frac{2 \sqrt{3x + 4} }{2 \sqrt{3x - 5} } = \frac{10}{8} \\ \frac{ \sqrt{3x + 4} }{ \sqrt{3x - 5} } = \frac{5}{4}</p><p></p><p></p><p>{(\frac{ \sqrt{3x + 4} }{ \sqrt{3x - 5} }) }^{2} = ( {\frac{5}{4}})^{2} \\ \frac{3x + 4}{3x - 5} = \frac{25}{16} \\ 48x + 64 = 75x - 125 \\ 48x - 75x = - 125 - 64 \\ - 27x = - 189 \\ x = \frac{189}{27} = 7</p><p>$

4.

$x = \frac{6ab}{a + b} \\ </p><p>\frac{ x + 3a }{x - 3a} + \frac{x + 3b}{x - 3b} </p><p>$

Solving above gives

$</p><p>\frac{2 {x}^{2} - 18ab }{(x - 3a)( x - 3b)}</p><p></p><p>$

Putting value of x

$\frac{ {2 \times( { \frac{6ab}{a + b} })^{2}} - 18ab }{( \frac{6ab}{a + b} - 3a)( \frac{6ab}{a + b} - 3b } \\ = \frac{ \frac{72 {a}^{2} {b}^{2} }{ {(a + b)}^{2} } - 18ab}{( \frac{6ab - 3 {a}^{2} - 3ab}{a + b} )( \frac{6ab - 3 {b}^{2} - 3ab}{a + b}) } \\ = \frac{ \frac{72 {a}^{2} {b}^{2} - 18ab {(a + b)}^{2}}{ {(a + b)}^{2} } }{( \frac{3ab - 3 {a}^{2} }{a + b})( \frac{3ab - 3 {b}^{2} }{a + b} )} \\ = \frac{18ab(4ab - ( {a}^{2} + {b}^{2} + 2ab) }{9ab(b - a)(a - b)} \\ = \frac{2(4ab - {a }^{2} - {b}^{2} - 2ab)}{(b - a)(a - b)} \\ = \frac{ - 2( {a}^{2} + {b}^{2} - 2ab) }{(b - a)(a - b)} \\ = \frac{ - 2 {(a - b)}^{2} }{(b - a)(a - b)} \\ = \frac{ - 2(a - b)}{(b - a)} \\ = \frac{2(b - a)}{(b - a)} \\ = 2$