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The solution of inequality (x+1)(x 2 +1) 1/2 >x 2 -1 is (a) {-1} U [2,infinite) (b) [-1,infinite) (c){-4}u[2,3] (d)(-5,infinite)

The solution of inequality (x+1)(x2+1)1/2>x2-1 is


(a) {-1} U [2,infinite)


(b) [-1,infinite)


(c){-4}u[2,3]


(d)(-5,infinite)

Grade:12

1 Answers

AskiitiansExpert Milanshu
9 Points
12 years ago


(x+1)(x2+1)1/2>x2-1

(x+1)(x2+1)1/2>(x-1)(x+1)

either x=-1 or

case 1:x>-1

(x2+1)1/2>x-1

squaring both side,

 

(x2+1)>x2+1 +2x

therefore x>0

case 2: x<-1

(x2+1)1/2<x-1

therefore, x<0

therefore, answer is [-1,infinte)

 

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