Question

Solve x : √2x+9 - √x+1 = √x-4​

Answer 1

Answer:

$4x - 4y22105? \times \frac{?}{?}$

Answer 2

Answer:

Required value of x is $98(3 + 2 \sqrt{2} )$

Step-by-step explanation:

Given equation,

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

$\sqrt{2} \times \sqrt{x} + 9 - \sqrt{x} + 1= \sqrt{x} - 4$

Let,$\sqrt{x} = y$

So,$\sqrt{2} \times y + 9 - y + 1 = y - 4$

We are separating variable and constant part,

$\sqrt{2} y - y - y = - 4 - 1 - 9$

$( \sqrt{2} - 2)y = - 14$

$y = - \frac{14}{ \sqrt{2} - 2 }$

$y = \frac{14}{2 - \sqrt{2} } = \frac{14(2 + \sqrt{2)} }{(2 - \sqrt{2})(2 + \sqrt{2} ) } = \frac{14(2 + \sqrt{2}) }{ {2}^{2} - { \sqrt{2} }^{2} } = \frac{14(2 + \sqrt{2} )}{4 - 2} = 7(2 + \sqrt{2} )$

Now

$y = \sqrt{x} = 7(2 + \sqrt{2} )$

$x = {7}^{2} {(2 + \sqrt{2}) }^{2} = 49(4 + 2 + 4 \sqrt{2} ) = 49(6 + 4 \sqrt{2} ) = 98(3 + 2 \sqrt{2} )$

Here applied formula,

${a}^{2} - {b}^{2} = (a + b)(a - b)$

Some other important formulas of Algebra ,

a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)