(3-2x)(3+2x) please solve it
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Secondary School Math 10 points
2x+3/2x-3+2x-3/2x+3=17/4, x≠+3/2,Solve the given quadratic equation using factorization.
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mysticd
mysticd Genius
Solution :
(2x+3)/(2x-3) + (2x-3)/(2x+3) = 17/4
=> [(2x+3)²+(2x-3)²]/[(2x+3)(2x-3)]=17/4
=> {2[(2x)²+3²]}/[(2x)²-3²] = 17/4
_________________________
We know the algebraic identities:
i )( a + b )² + ( a - b )² = 2( a² + b² )
ii ) ( a + b )( a - b ) = a² - b²
__________________________
=> [2(4x²+9)]/(4x²-9) = 17/4
=>( 8x²+18)/(4x²-9) = 17/4
=> 4(8x²+18) = 17(4x²-9)
=> 32x²+72 = 68x² - 153
=> 32x² - 68x² = -153 - 72
=> -36x² = -225
=> x² = ( -225 )/(-36 )
=> x² = 225/36
=> x = ± √225/36
=> x = ± 25/6
Therefore ,
-(25/6 ), 25/6 are roots of given
quadratic equation.