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ajay agarwal Grade:
        

If y=squareroot(x/a)+squareroot(a/x) , then show that 2xydy/dx=(x/a-a/x)

6 years ago

Answers : (3)

melvin davis
6 Points
										

y^2 = x/a+a/x+2  ====================             a xy^2 = x^2+a^2      =====================           a2xydy/dx+ay^2 = 2x


2xydy/dx = x/a+x/a - y^2  ====================          x/a+x/a-x/a-a/x-2  =====================     x/a-a/x-2 = 2xydy/dx


so there may be any mistake in that qusetion

6 years ago
vikas askiitian expert
510 Points
										

y = (x/a)1/2 + (a/x)1/2 ...............1




dy/dx = d/dx(x/a)1/2 + d/dx(a/x)




         =[(1/a)1/2  d/dx (x1/2) ]+ [ a1/2 d/dx (1/x)1/2 ]




         =(1/a)1/2 (1/2) (1/x)1/2  +  a1/2(-1/2) (1/x)3/2




multiplying this eq by 2xy




2xydy/dx = (1/a)1/2 .x1/2. y  -   a1/2 .(1/x)1/2 y




             = y[ (x/a)1/2 - (a/x)1/2]         ..............2




from eq 1 putting y in eq 2




             =[(x/a)1/2 + (a/x)1/2].[(x/a)1/2-(a/x)1/2]




             =[x/a - a/x]

6 years ago
Surbhi Kumari
29 Points
										

FIRST  FIND dy/dx.


MULTIPLY IT BY TWO.


ALSO Y=(x+a)/sqrt(ax).......1


NOW IF GO IN REVERSE THEN U HAVE TO PROVE THAT


2dy/dx=(x^2-a^2)/ayx^2


        now replace  y by equ 1


on simplifiation u would get the expression same as 2dy/dx 


 

6 years ago
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