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The range of x^2-x+1/x^2+x+1 , x belong to R is

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Solution:

$y=fracx^2-x+1x^2+x+1Rightarrow (y-1)x^2+(y+1)x+y-1=0$

$Delta geq 0Rightarrow (y+1)^2-4(y-1)^2geq 0$

$[y+1+2(y-1)][y+1-2(y-1)]geq 0$

$Rightarrow$ $(3y-1)(y-3)leq 0$ , $yin[frac13,3].$

Posted by

Deependra Verma

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