13Confusion not solved yet....!!
The no. of irrational solutions of the equation -
\sqrt{x^2 + \sqrt{x^2 + 11}} + \sqrt{x^2 - \sqrt{x^2 + 11}} = 4
are - a) 0 b) 2 c) 4 d) Infinite
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12 Answers
62Wow this one was a googley :P
I spent atleast 10 minutes thinking on this one..
The answer is zero because the part \sqrt{x^2-\sqrt{x^2+11}} is never real :D
While the other part is always real for any real value of x..
Thus there is no real root for the equation.
Thus there is no rational root :P
19where did u practice to face these googlies so well? MCG or LORDS? .....;)
341x = \pm \sqrt 5 are solutions. (symmetry and monotonic behaviour for x>0 mean no other solutions exist)
If under the square-root there were x4 then we could have called it googley!
62Oops [3] [1]
Itne din baad I gave a couple of answers today and those too with mistakes [2]
13But sir, how do v go about finding its solutions ?
V can take x2 + 11 =y2 so tht it becomes -
√y2 + y -11 + √y2 - y -11 = 4
Wat to do after tht ?....
13Waise, it will solved by the usual Shifting n Squaring method [3] .... but a shorter one wud be better...
62I was thinking of rationalizing and getting two simultaneous equations...
but that does not seem to help a lot.
13Haan, yes bhaiya !....Rationalisation helped too but tht solution is nearly of the same length...
But v get x = ± √5 ...then why is the ans given to be - c) 4 ....?
341wait, is this function not increasing for x>0? How come four roots then?