1.

Solve` (x^2 -x-1) (x^2-x-7) lt -5`

Answer» ` (x^2 -x-1) (x^2-x-7) +5 lt 0 `
Let `x^2-x=y`
` rArr (y-1)(y-7)+5 lt 0 `
`rArr y^2-8y + 12 lt 0 `
or `(y-6)(y-2) lt 0 `
`rArr 2 lt y lt 6 `
`rArr 2 lt x^2 -x lt 6 `
Now `x^2 - x - gt 2`
or `(x-2) ( x+1) gt 0 `
or `(x-2)(x+1) gt 0 `
`rArr x in (- oo , -1 ) cup (2, oo) `
`x^2-x-6 lt 0 `
`rArr ( x-3)(x+2) lt 0 `
`rarr x in (-2 , 3)`
Form (1) and (2) common values of `x are x in (-2, -1) cup (2,3)`


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