This one is kind of easy
x 3 + 2 x 2 − 7 x + 6 = x 3 + 1 + x
Solve for x .
The answer is 0.5.
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2 solutions
Now that's one way to solve this problem. But before you square them, make sure it is stated that x ≥ 0
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You're welcome. And please try to solve this in other ways because not all equations end up with something as simple as 0.5. It could be 1 + 2 or worse. Just keep on trying :)
How did u get (2x-1) as a factor or how did u factorize the equation :)
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I did do the breakoff but forgot to arrange it.
3 2 x 3 - 6 8 x 2 + 50x - 1 6 x 2 + 34x - 25 = 0.
2x ( 1 6 x 2 - 34x + 25 ) -1 ( 1 6 x 2 - 34x + 25 ) = 0
(2x-1)( 1 6 x 2 - 34x + 25 ) :)
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In response to Rwit Panda : Is this a matter of observation or some technique ??
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@Chirayu Bhardwaj – To me, is only an observation.
There may very well be a set procedure to it but I am unaware of any. :)
We square on both sides and then again square to remove all square roots.
But for this x>=0 when we remove square roots.
We obtain the equation 3 2 x 3 - 8 4 x 2 + 84x - 25 = 0.
3 2 x 3 - 6 8 x 2 - 1 6 x 2 + 50x + 34x - 25 = 0.
(2x-1)( 1 6 x 2 - 34x + 25) = 0
This clearly shows that it has one real value of x at x= 0.5
Other values of x are complex, which would not satisfy due to presence of square roots.
Hence answer is x = 0 . 5