Range of\[f(x)=\sqrt{x^2+x+2}-\sqrt{x^2+x+1}\]

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Range of\[f(x)=\sqrt{x^2+x+2}-\sqrt{x^2+x+1}\]

Mathematics
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\[f(x)=\sqrt{x^2+x+2}-\sqrt{x^2+x+1}\]
yeah
Range = Real Numbers

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I think |dw:1347709678855:dw|
thats it
what is ur approach?
always positive, diff for max
x^2+x+2=(x+1/2)^2 +7/4 x^2+x+1=(x+1/2)^2+3/4 Now, f(x) is maximum when (x+1/2)^=0 because the f(x) value decresases as (x+1/2)^2 is greater than 0 since |dw:1347710167952:dw| Now, when (x+1/2)^2 ---->approaches infinity f(x) will be minimum but will never be zero.....but will be very close to zero
Sorry not good at expalining things
But I think thats it
\[f(x)=\frac{1}{\sqrt{x^2+x+2}+\sqrt{x^2+x+1}}\]
Is that another question?
no this is same
?
\[f(x)=\sqrt{x^2+x+2}-\sqrt{x^2+x+1}\times\frac{\sqrt{x^2+x+2}+\sqrt{x^2+x+1}}{\sqrt{x^2+x+2}+\sqrt{x^2+x+1}}\]
just rationalizing the denom, isn't it ?
yes
Oh ya

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