Question

if a/b​=b/c=c/d=d/a, prove a/c=(a^2+b^2)/(b^2+c^2)​

Answer 1

Step-by-step explanation:

Hey Mate !!

Here is your solution :

Given,

=> a + c = 2b

=> a = 2b - c ---------- ( 1 )

And,

=> ( 1/b ) + ( 1/d) = 2/c

Taking L.C.M of b and d.

=> ( d + b )/bd = 2/c

=> ( b + d ) = 2bd/c

=> b = ( 2bd / c ) - d

=> b = ( 2bd - dc )/c

Taking out d as common,

=> b = d ( 2b - c )/ c -------- ( 2 )

Now, by divding ( 1 ) by ( 2 ),

=> a/b = ( 2b - c ) ÷ { d( 2b - c ) /c }

=> a/b = { ( 2b - c ) × c } ÷ { d ( 2b - c ) }

=> a/b = c/d

★ Proved ★

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Hope it helps !! ^_^