If a > 1, b > 1 then (a+1)(b+1)>2(ab+1) ?

byAmlesh Mahato •October 09, 2020

0

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Solution:

⇨Given $If a > 1, b > 1 then (a+1)(b+1)>2(ab+1) ?$

$\therefore a+1>2$ .........(i)

⇨Similarly $b>1$

$\therefore b+1>2$ ........(ii)

⇨Adding equation (i)+(ii)

$\Rightarrow (a+1)(b+1)>4$ .......(iii)

⇨Again $ab>1$

$\therefore ab+1>2$ . .............(iv)

⇨Dividing equation (iii) by (iv)

$\therefore \frac{(a+1)(b+1)}{ab+1}>\frac{4}{2}$

$\Rightarrow \frac{(a+1)(b+1)}{ab+1}>2$

$\Rightarrow (a+1)(b+1)>2(ab+1)$ Proved

Tags: Advance Math Class 8

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