Question

solve it with explainations 12 no
^_^
urgent i need the ans quickly

Answer 1

Sol : The answer is option ( d ) √xy = √x √y

Explanation : For option ( a ),

 √x - √y = √( x - y )

 By squaring both sides ,

 ( √x - √y )² = √( x - y )²

 ( √x )² + ( √y )² - 2 * √x * √y = x - y 

 x + y - 2 * √x * √y = x - y

 x + y - x + y = 2 * √x * √y

 2 y = 2 * √x * √y

  y = √ x * √y

 y / √y = √x

 √y = √x

 y = √x²

 y = x.

But it is given that y < x.So, it is incorrect.

For option ( b ),
 
 √x + √x =  √( 2x )

 By taking √x common in L.H.S ,

  √x( 1 + 1 ) =  √( 2 x )

 √x  ( 2 ) = √( 2 x )

  { √x ( 2 ) }² = 2 x

  4 x = 2 x

 4 x - 2 x = 0
 
 2 x = 0

  x = 0 / 2

  x = 0.

But it is given that 0 < x , hence it is also incorrect .

For option ( c ),

 x√y = y√x

 x = y√x / √y

 x = √ y . √x

 x / √x = √y

 √x = √y

 x = (√y)²

 x = y.

But it is given that y < x .So, it is not possible.

For option ( d ),

 √( xy ) = √x * √y


 √( xy ) = x^ ( 1/2) * y^( 1/2)     { √a = a^(1/2) }

 √( x y ) = ( x y )^( 1/2 )           { m^a * n^a = ( mn )^a }

  √(xy ) = √(xy)                        { a^(1/2) = √a }

  xy = xy

So, it is possible .

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