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Question
If x=4aba+b then value of x+2ax−2a+x+2bx−2b
If x=4aba+b then value of x+2ax−2a+x+2bx−2b
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Solution
The correct option is A 2
Given, x=4ab/(a+b)=> x=2a×2b/(a+b)=> x/2a=2b/(a+b)Using componendo and dividendo => x+2a/x−2a=2b+a+b/2b−a−b=> x+2a/x−2a=3b+a/b−a
Similarly, x+2b/x−2b=3a+b/a−b
Now, adding both,[x+2a/x−2a]+[x+2b/x−2b]=[3b+a/b−a]+[3a+b/a−b]RHS => [3b+a/b−a]−[3a+b/b−a]=> 3b+a−3a−b/b−a=> 2b−2a/b−a=> 2(b−a)/b−a=> 2
Hence, LHS =2
Given, x=4ab/(a+b)
=> x=2a×2b/(a+b)
=> x/2a=2b/(a+b)
Using componendo and dividendo
=> x+2a/x−2a=2b+a+b/2b−a−b
=> x+2a/x−2a=3b+a/b−a
Similarly, x+2b/x−2b=3a+b/a−b
Now, adding both,
[x+2a/x−2a]+[x+2b/x−2b]=[3b+a/b−a]+[3a+b/a−b]
RHS => [3b+a/b−a]−[3a+b/b−a]
=> 3b+a−3a−b/b−a
=> 2b−2a/b−a
=> 2(b−a)/b−a
=> 2
Hence, LHS =2
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