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Properties of Inequalities

| x ∧ 2-1|+ x...

Question

|x^2 -1| +x+1 =0

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Solution

case (i)

-1<x<1

x^2-1 <0: |x^2-1| = -(x^2-1)

therefore -x^2+1+x+1=0

-x^2+x+2=0

by solving the equation

we get x= 2, -1

as this is outside our limit (-1<x<1)

they are not the solution

case(ii)

x=or >1 or x < or = -1

therefore x^2-1>0 : |x^2-1| = x^2-1

x^2-1+x+1=0

x^2+x =0

x(x+1) =0

therefore x= 0 , -1

0 is not an answer as it is outside the limit

so solutuion for the given quation is -1

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