Just expand it , and try to put in square form , its very simple
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Shivang Jindal
·
3 years, 11 months ago

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@Shivang Jindal
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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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Calvin Lin
Staff
·
3 years, 11 months ago

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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Aditya Kumar
·
3 years, 11 months ago

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@Aditya Kumar
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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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Calvin Lin
Staff
·
3 years, 11 months ago

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thanks i have now solved it
–
Aditya Kumar
·
3 years, 11 months ago

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As a hint : If \(x, y >1 \), then \( (x-1)(y-1) > 0 \) so \( xy + 1 > x + y \). Use this many times. – Calvin Lin Staff · 3 years, 11 months ago

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Try to substitute \(x=a-1, y=b-1, z=c-1, w=d-1\). – Shourya Pandey · 3 years, 11 months ago

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– Tim Vermeulen · 3 years, 11 months ago

Don't you mean \(x=a+1,y=b+1\), etcetera?Log in to reply

– Shourya Pandey · 3 years, 11 months ago

Try doing it, it becomes very easyLog in to reply

– Shourya Pandey · 3 years, 11 months ago

NoLog in to reply

Just expand it , and try to put in square form , its very simple – Shivang Jindal · 3 years, 11 months ago

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– Calvin Lin Staff · 3 years, 11 months ago

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.Log in to reply

– Shivang Jindal · 3 years, 11 months ago

I think, its from Challenge and thrill . right?Log in to reply

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 – Aditya Kumar · 3 years, 11 months ago

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This looks very similar to the inequality, especially on the LHS. Use this many times. – Calvin Lin Staff · 3 years, 11 months ago

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thanks i have now solved it – Aditya Kumar · 3 years, 11 months ago

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