# 8(abcd+1)>(a+1)(b+1)(c+1)(d+1) prove it

if a,b,c,d,all are greater than 1

6 years, 2 months ago

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What 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.

Staff - 6 years, 2 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

- 6 years, 2 months ago

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.

Staff - 6 years, 2 months ago

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

- 6 years, 2 months ago

I think, its from Challenge and thrill . right?

- 6 years, 2 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.

Staff - 6 years, 2 months ago

Can someone explain it once more??...

- 1 year, 10 months ago

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

- 6 years, 2 months ago

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

- 6 years, 2 months ago

No

- 6 years, 2 months ago

Try doing it, it becomes very easy

- 6 years, 2 months ago

thanks i have now solved it

- 6 years, 1 month ago