Question

1 1 1<br />-=-+-+-<br />a+b+xabx<br />+ b # 0 को गुणनखण्ड विधि द्वारा<br />द्विघात समीकरण<br />हल कीजिए।​

Answer 1

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(1/ [a+b+x]) = (1/a) +( 1/b )+ (1/x)

( 1 / [a+b+x] ) - (1 / x ) = (1/a) + (1/b)

=> { x - [a+b+x] } / ([a+b+x] * x ) = {a+b} / ab

=> - { a+b} / ( [a+b+x] * x ) = { a+b} / ab

=> -1 / ( [a+b+x] * x ) = 1 / ab

Cross Multiply : -ab = [a+b+x] * x

On Simplification : x2 + (a+b) x + ab = 0

Applying the Splitting the middle term method :

=> x2 + (a+b) x + ab = 0

=> [x2 + ax]+ [b x + ab] = 0

So : x ( x + a) + b ( x + a) = 0

=> (x + a ) * ( x + b ) = 0

Therefore : (x+a) = 0 or (x+b) = 0

Now : x = (-a) or x = (-b)

The value of x is : (-a) or (-b)

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