Question

The set of values of 'x' satisfying (x²-x-1)(x²-x-7)<-5 is (a,b)U(c,d) then a+b+c+d is equal to

Answer 1

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(x

2

−x−1)(x

2

−x−7)<−5

Let x

2

−x be t

(t−1)(t−7)<−5

t

2

−8t+7+5<0

t

2

−8t+12<0

(t−6)(t−2)<0

(x

2

−x−6)(x

2

−x−2)<0

(x−3)(x+2)(x−2)(x+1)<0

x∈(−2,−1)∪(2,3)