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Find the value of lambdaif2x^2+7x y+3y^2...

Find the value of `lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0` represent a pair of straight lines.

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The equation `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` respresents a pair of lines if `abc+2fgh-af^(2)-bg^(2)-bc^(2)=0`. So , for given equation ,
`6lambda+2(7)(4)((7)/(2))-2(7)^(2)-3(4)^(2)-lambda((7)/(2))=0` or
`6lambda+196-98-48-(49lambda)/(4)=0`
or`(49lambda)/(4)-6lambda=196-146=50`
or `(25lambda)/(4)=50`
or `lambda=(200)/(25)=8`
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