# 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

123 Points
4 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+b  =   $< a+\sqrt{a^{}2-4b^{}2}/4b> - < a^{}2 + )}a \sqrt{a^{}2- 4b^{}2}/2> + b^{}2$

which ,  ultimately becomes zero. hence, proved.