Question

Solve it Guys __________,_

I stuck in it


Challenging Question_______​

Answer 1

Solution:

$\sf{ \implies{2 \sqrt{x + 5} - \sqrt{2x + 8} =2}}$

$\sf{ \implies{2 \sqrt{x + 5} = \sqrt{2x + 8} + 2}} \\ \\ \sf{ \implies{( {2 \sqrt{x + 5}) }^{2} = ( { \sqrt{2x + 8} +2) }^{2}}} \\ \\ \sf{ \implies{4(x + 5) = 2x + 8 + 4 + 2. \sqrt{2x + 8}.2}} \\ \\ \sf{ \implies{4x + 20 = 2x + 12 + 4. \sqrt{2x + 8}}} \\ \\ \sf{ \implies{4x - 2x + 20 - 12 = 4 \sqrt{2x + 8}}} \\ \\ \sf{ \implies{2x + 8 =4 \sqrt{2x + 8}}} \\ \\ \\ \sf{ \implies{ \green{squaring \: on \: both \: sides}}} \\ \\ \sf{ \implies{( {2x + 8)}^{2} = 16(2x + 8)}} \\ \\ \sf{ \implies{ {4x}^{2} + 64 + 32x = 32x + 128}} \\ \\ \sf{ \implies{ {4x}^{2} + 32x -3 2x + 64 - 128 = 0}} \\ \\ \sf{ \implies{ {4x}^{2} - 64= 0}} \\ \\ \sf{ \implies{ {4x}^{2} = 64}} \\ \\ \sf{ \implies{ {x}^{2} = \frac{64}{4}}} \\ \\ \sf{ \implies{ {x}^{2} = 16}} \\ \\ \sf{ \implies{x = 4}}$

Therefore, Value of $\sf{2 \sqrt{x + 5} - \sqrt{2x + 8} =2 is 4}$

Answer 2

Answer : x = 4

Step by step explanation :

Given equation :

2 (√x + 5) - √( 2x + 8 ) = 2

Taking the term (√2x + 8 ) to the R.H.S ,

2√(x + 5) = 2 + (√2x + 8)

Now,  In order to remove the square roots, Square both sides -

[ 2√(x + 5) ]^2 =[ (√2x + 8) + 2 ]^2

Using the identity [ in R.H.S ]

a^2 + 2ab + b^2 = ( a + b )^2, we get :

4 ( x + 5 ) = 2x + 8 + 4 + 2 × ( √2x + 8 ) × 2

4x + 20 = 2x + 12 + 4( √2x + 8 )

Simplifying the equation further,

4x - 2x = 12 - 20 + 4((√2x + 8))

2x = -8 + (  4 √2x + 8 )

2x + 8 = 4 √2x + 8

Here, Squaring both the sides, we get :

( 2x + 8 )^2 = 16 × (2x + 8)

Taking the term ( 2x + 8 ) to L.H.S , we get :

2x + 8 = 16

2x = 8

x = 4

Thus,  The value of x is 4 .

Required answer : x = 4

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