Question

Let x and y be the 2 real numbers satisfying y= (2008x +2009/2010x-2011)^1/2 + (2008x+2009/2011-2010x)^1/2 ​

Answer 1

SOLUTION

TO DETERMINE

Let x and y be the 2 real numbers satisfying

$\displaystyle \sf{y = \sqrt{ \frac{2008x + 2009}{2010x - 2011} } + \sqrt{ \frac{2008x + 2009}{2011 - 2010x } } }$

EVALUATION

Here it is given that

$\displaystyle \sf{y = \sqrt{ \frac{2008x + 2009}{2010x - 2011} } + \sqrt{ \frac{2008x + 2009}{2011 - 2010x } } }$

Let us assume that

$\displaystyle \sf{a = \frac{2008x + 2009}{2010x - 2011} }$

Then above becomes

$\displaystyle \sf{y = \sqrt{ a} + \sqrt{ - a } }$

Since y is a real number

Thus we get

$\displaystyle \sf{ a \geqslant 0 \: \: and \: \: - a \leqslant 0 }$

Which gives a = 0

Consequently we get y = 0

FINAL ANSWER

Hence the required value of y = 0

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