Find the integral value of x such that 3 x-1-x-1-x-1-3 x-1-5-2A- 2B- 4C- 5D- None of these

The correct option is D None of these Let (3x+1)/(x+1) = p p +1/p = 5/2 2p^2+2 = 5p 2p^2 5p + 2 =0 2p^2 4p p + 2 =0 (2p 1)(p 2) =0 p = 1/2 , p = 2 Substitut ...

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Standard X

Mathematics

Rational Expression

Find the inte...

Question

$F i n d t h e i n t e g r a l v a l u e o f x s u c h t h a t \frac{3 x + 1}{x + 1} + \frac{x + 1}{3 x + 1} = \frac{5}{2}$

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Solution

The correct option is D
None of these

Let \frac{(3x+1)}{(x+1)} = p

$p + \frac{1}{p} = \frac{5}{2}$

$2 p^{2} + 2 = 5 p$

$2 p^{2} - 5 p + 2 = 0$

$2 p^{2} - 4 p - p + 2 = 0$

$(2 p - 1) (p - 2) = 0$

$p = 1 / 2, p = 2$

$S u b s t i t u t i n g, t h e v a l u e o f p i n e q u a t i o n (i) w e g e t$

$\frac{3 x + 1}{x + 1} = 2 \frac{x + 1}{3 x + 1} = 2$

$x = 1 x = \frac{- 1}{5}$

$S o, t h e v a l u e s o f x a r e 1 a n d \frac{- 1}{5}$

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Find the integral value of x such that 3x+1x+1+x+13x+1=52

The correct option is D None of these Let \frac{(3x+1)}{(x+1)} = p p+1p=52 2p2+2=5p 2p2−5p+2=0 2p2−4p−p+2=0 (2p−1)(p−2)=0 p=1/2,p=2 Substituting, the value of p in equation (i) we get 3x+1x+1=2 x+13x+1=2 x=1 x=−15 So, the values of x are 1 and −15

$F i n d t h e i n t e g r a l v a l u e o f x s u c h t h a t \frac{3 x + 1}{x + 1} + \frac{x + 1}{3 x + 1} = \frac{5}{2}$