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If x= under root a+2b + under root a-2b/ under root a+2b - under root a-2b prove that b^2x^2-abx+b^2=0

If x= under root a+2b + under root a-2b/ under root a+2b - under root a-2b prove that b^2x^2-abx+b^2=0

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1 Answers

ADARSH SINGH
123 Points
5 years ago
x =\sqrt{ a+2b }+\sqrt{ a-2b} / (\sqrt{a+2b }-\sqrt{ a-2b})
 
rationalising the given equation, we will get ,(note; to rationalise, divide and multiply whole equation by it’s rationalising factor.)
 
x = a+\sqrt{ a^{}2-4b^{}2}/2b
 
substitute this value in given equation , and you will get following :-
 
b2x2-abx+b2   =   < a+\sqrt{a^{}2-4b^{}2}/4b> - < a^{}2 + )}a \sqrt{a^{}2- 4b^{}2}/2> + b^{}2
 
which ,  ultimately becomes zero. hence, proved.
 
 
 

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