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

Question

melvin davis · Answer

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

vikas askiitian expert · Answer

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 (x 1/2 ) ]+ [ a 1/2 d/dx (1/x) 1/2 ] =(1/a) 1/2 (1/2) (1/x) 1/2 + a 1/2 (-1/2) (1/x) 3/2 multiplying this eq by 2xy 2xydy/dx = (1/a) 1/2 .x 1/2 . y - a 1/2 .(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]

Surbhi Kumari · Answer

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

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

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

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