Question

$I'm sure only less than 1\% of you can solve this problem.$

$If you find this, then you'll be the very brilliant and genius in the whole world. \\ \\ And also I'm giving you 50 points each. \\ \\ So I'm challenging.$

$Found this question and reason yesterday. Not from any other sources. The question's on my own. \\ \\ \\ Okay.$

$Consider the equality given below.$

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

$By cross multiplication, we get,$

$(3x+1)(3x+1) = (3x+2)(3x+2) \\ \\ \Rightarrow (3x+1)^2=(3x+2)^2$

$By taking their square roots, we get,$

$3x+1=3x+2$

$By subtracting \ 3x\ from both sides, we get,$

$1=2$

$How is this possible?! \\ \\ Find where I'd mistaken. \\ \\ Also find the real value of \ x.$

$If you find it, then you'll be the real \ \bold{`brainliest} '!!! \\ \\ \\ SO I'M CHALLENGING!!!$

$\#adithyasajeevan$

Answer 1

Answer:

x = -1/2

Not using latex to save time .

Hope it helps !

Step-by-step explanation:

First of all it is given that :

( 3 x + 1 ) / ( 3 x + 2 ) = ( 3 x + 2 ) / ( 3 x + 1 )

Let ( 3 x + 1 ) / ( 3 x + 2 ) be t

So :

t = 1 / t

⇒ t² = 1

⇒ t = ± 1

( 3 x + 1 ) / ( 3 x + 2 ) = ± 1

⇒ 3 x + 1 = either ( 3 x + 2 )

Or ⇒ 3 x + 1 = - ( 3 x + 2 )

Considering : 3 x + 1 = - 3 x - 2

⇒ 6 x = -2 - 1

⇒ x = -3/6

⇒ x = -1/2

Hence x = -1/2

Now see the first one :

3 x + 1 = 3 x + 2

First of all this is not possible because 1 ≠ 2

Hence this should not be considered .

Now :

( 3 x + 1 )² = ( 3 x + 2 )²

Next step is WRONG :

Whenever x² = a²

either x = a OR x = - a

x may not be a !

Eg :

( 5 )² = ( - 5 )²

We cannot say 5 = - 5 .

When x² = a² |x| = |a| !

And this was a problem that even bad students can solve . It is not so complex .

This is the basis of mathematics problems .

It cannot be said difficult at all .

This is the main Point ^^"

Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

Kindly verify my answer!

Hope this attachment helps you.