The set of real number x for which x2-|x+2|+x>0 is

a)(-infinity,-2)U(2,infinity)

b)(-infinity,squre root of 2)U(square root of 2,infinity)

c)(-infinity,-1)U(1,infinity)

d)(square root of 2,infinity)

Asked by Abhilasha T. | 16th May, 2014, 12:09: AM

Expert Answer:

Consider,
x squared minus open vertical bar x space plus space 2 close vertical bar space plus space x greater than 0 C a s e space 1 : space x space plus space 2 space space greater than space 0 rightwards double arrow space x squared space minus space x space minus space 2 space plus space x space greater than space 0 rightwards double arrow space x squared minus 2 space greater than space 0 rightwards double arrow x space greater than space square root of 2 space space o r space x space less than space minus square root of 2 x space element of space open parentheses minus 2 comma space minus square root of 2 close parentheses union open parentheses square root of 2 comma space infinity close parentheses space C a s e space 2 : space space x space plus space 2 space space less than space 0 rightwards double arrow space x squared space plus space space x space plus space space 2 space plus space x space greater than space 0 rightwards double arrow space open parentheses x plus 1 close parentheses squared plus 1 space greater than space 0 W h i c h space i s space t r u e space f o r space x space less than space minus 2 T h e r e f o r e comma space x element of open parentheses minus infinity comma space minus square root of 2 close parentheses space union space open parentheses square root of 2 comma space infinity close parentheses
Hence, the option 'A' is correct.

Answered by Avinash Soni | 16th May, 2014, 09:23: AM

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