Question

Please solve the question

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

0.

Step-by-step explanation:

Given,

x = [ √( m + n ) + √( m - n ) ] / [ √( m + n ) - √( m - n ) ]

= > x / 1 = [ √( m + n ) + √( m - n ) ] / [ √( m + n ) - √( m - n ) ]

Using componendo & dividendo :

= > ( x + 1 ) / ( x - 1 ) = [ { √( m + n ) + √( m - n

) } + { √( m + n ) - √( m - n ) } ] / [ { √( m + n ) + ( m - n ) } - { √( m + n ) - √( m - n ) } ]

= > ( x + 1 ) / ( x - 1 ) = [ 2√( m + n ) ] / [ 2√( m - n ) ]

= > ( x + 1 ) / ( x - 1 ) = √( m + n ) / √( m - n )

Square on both sides :

= > ( x + 1 )^2 / ( x - 1 )^2 = ( m + n ) / ( m - n )

= > ( m - n )( x + 1 )^2 = ( m + n )( x - 1 )^2

= > ( m - n )( x^2 + 1 + 2x ) = ( m + n )( x^2 + 1 - 2x )

= > mx^2 + m + 2mx - nx^2 - n - 2nx = mx^2 + m - 2mx + nx^2 + n - 2nx

= > 2mx - nx^2 - n = - 2mx + nx^2 + n

= > 2nx + 2nx - nx^2 - nx^2 - n - n = 0

= > 4nx - 2nx^2 - 2n = 0

= > 2nx^2 - 4mx + 2n = 0

= > nx^2 - 2mx + n = 0

Hence the numeric value of given expression is 0.