Question

Find the positive square root of (2x*2+5x+2)(x*2-4)(2x*2-3x-2).

Answer 1

Solution :

i ) 2x² + 5x + 2

= 2x² + 4x + x + 2

= 2x( x + 2 ) + 1( x + 2 )

= ( x + 2 )( 2x + 1 )

ii ) x² - 4

= x² - 2²

= ( x + 2 )( x - 2 )

iii ) 2x² - 3x - 2

= 2x² - 4x + x - 2

= 2x( x - 2 ) + 1( x - 2 )

= ( x - 2 )( 2x + 1 )

Now ,

√(2x²+5x+2)(x²-4)(2x²-3x-2)

=√(x+2)(2x+1)(x+2)(x-2)(x-2)(2x+1)

= (x+2)(x-2)(2x+1)

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