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All the values of m for which both roots...

All the values of m for which both roots of the equation `x^(2)-2 m x+(m^(2)-1)=0` are greater than -2 but less than 4 lie in the interval

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Let `f(x)=x^(2)-2mx+x^(2)-1`, as exactly one root of `f(x)=0` lies in the interval `(-2,4)`, we can take `Dgt0` and `f(-2)f(4)lt0`.
(i) Consider `Dgt0`
`(-2m)^(2)-4.1(m^(2)-1)gt0implies4gt0`
`:. m epsilonR`……………i
(ii) Consider `f(-2)f(4)lt0`
`(4+4m+m^(2)-1)(16-8m+m^(2)-1)lt0`
`implies(m^92)+4m+3)(m^(2)-8m+15)lt0`
`implies(m+1)(m+3)(m-3)(m-5)lt0`
`implies(m+3)(m+1)(m-3)(m-5)lt0`

`:.m epsilon(-3,-1)uu(3,5)`.........ii
Hence the values fo `m` satisfying Eq. (i) and (ii) at the same time are `m epsilon (-3,-1)uu(3,5)`.
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