this question was from the beginning section of the book in inequalities so it does not require any prerequisities so i tried so solve this without am gm inequalitiy or any other but cannot solve it

I agree with just expand it. I'm not so sure what you mean by square form, though there is a way to write it as the sum of several positive (non-negative) terms.

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## Comments

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TopNewestWhat have you tried? What do you know?

As a hint : If $x, y >1$, then $(x-1)(y-1) > 0$ so $xy + 1 > x + y$. Use this many times.

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this question was from the beginning section of the book in inequalities so it does not require any prerequisities so i tried so solve this without am gm inequalitiy or any other but cannot solve it

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As a hint : If $x,y>1$, then $(x-1)(y-1)>0$ so $xy+1>x+y$.

This looks very similar to the inequality, especially on the LHS. Use this many times.

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Just expand it , and try to put in square form , its very simple

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I think, its from Challenge and thrill . right?

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I agree with just expand it. I'm not so sure what you mean by square form, though there is a way to write it as the sum of several positive (non-negative) terms.

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Can someone explain it once more??...

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Try to substitute $x=a-1, y=b-1, z=c-1, w=d-1$.

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Don't you mean $x=a+1,y=b+1$, etcetera?

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No

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Try doing it, it becomes very easy

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thanks i have now solved it

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