Question

Solve the following quadratic equations by factorization method.

Answer 1

HELLO DEAR,


x/(x + 1) + (x + 1)/x = 34/15

(x² + x² + 1 + 2x)/(x² + x) = 34/15

30x² + 30x + 15 = 34x² + 34x

4x² + 4x - 15 = 0

4x² + 10x - 6x - 15 = 0

2x(2x + 5) - 3(2x + 5) = 0

(2x + 5)(2x - 3) = 0

x = 3/2 , x = -5/2


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Solution :

x/(x+1) + (x+1)/x = 34/15

=> [x² + ( x + 1 )² ]/[(x+1)x]=34/15

=> ( x²+x²+2x+1)/(x²+x) = 34/15

=> 15( 2x² + 2x + 1 ) = 34( x² + x )

=> 30x² + 30x + 15 = 34x² + 34x

=> 0 = 34x² + 34x - 30x²-30x-15

=> 4x² + 4x - 15 = 0

Splitting the middle term ,

=> 4x² + 10x - 6x - 15 = 0

=> 2x( 2x + 5 ) - 3( 2x + 5 ) = 0

=> ( 2x + 5 )( 2x - 3 ) = 0

=> 2x + 5 = 0 or 2x - 3 = 0

2x = -5 or 2x = 3

x = -5/2 or x = 3/2

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