If-a-b-c-d-gt-0-And-1-a-1-2-b-1-3-c-1-4-d-1-1-Then-find-a-a-1-2b-b-1-3c-c-1-4d-d-1-

Question Number 173377 by Shrinava last updated on 10/Jul/22

If a, b, c, d > 0

And \frac{1}{a + 1} + \frac{2}{b + 1} + \frac{3}{c + 1} + \frac{4}{d + 1} = 1

Then find \frac{a}{a + 1} + \frac{2 b}{b + 1} + \frac{3 c}{c + 1} + \frac{4 d}{d + 1}

Answered by Rasheed.Sindhi last updated on 10/Jul/22

\begin{matrix} \underset{\underset{}{And \frac{1}{a + 1} + \frac{2}{b + 1} + \frac{3}{c + 1} + \frac{4}{d + 1} = 1}}{If a, b, c, d > 0} \end{matrix}

\frac{a}{a + 1} + \frac{2 b}{b + 1} + \frac{3 c}{c + 1} + \frac{4 d}{d + 1}

= \frac{a}{a + 1} - 1 + \frac{2 b}{b + 1} - 2 + \frac{3 c}{c + 1} - 3 + \frac{4 d}{d + 1} - 4 + 10

= \frac{- 1}{a + 1} + \frac{- 2}{b + 1} + \frac{- 3}{c + 1} + \frac{- 4}{d + 1} + 10

= - (\frac{1}{a + 1} + \frac{2}{b + 1} + \frac{3}{c + 1} + \frac{4}{d + 1}) + 10

= - (1) + 10 = 9

Commented by mr W last updated on 10/Jul/22

n i c e s o l u t i o n s i r!

Commented by Rasheed.Sindhi last updated on 10/Jul/22

T h a n k s a l o t s i r!

Commented by Shrinava last updated on 10/Jul/22

perfect professor thank you