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Find the set of positive values of b for...

Find the set of positive values of `b` for which the origin and the point (1, 1) lie on the same side of the straight line, `a^2x+ab y+1=0,AAa in Rdot`,b>0

Text Solution

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Points (0,0) and (1,1) lie on same side of the line `a^(2) x +aby + 1= 0.`
From (0,0).
`a^(2)(0) + ab(0) + 1 gt 0`
Therefore, for (1,1), we must have
`a^(2) +ab + 1 gt 0 " " AA a in R`.
`therefore D lt 0`
`therefore b^(2)-4 lt 0`
` " or " b in (-2,2)`
` "But " b gt 0`
`therefore b in (0,2)`
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