If x &#x2212;<!-- − --> <msqrt> 2 x </mfrac> </msqrt> = 3 then

grenivkah3z

grenivkah3z

Answered question

2022-07-04

If x 2 x = 3 then x 2 x = ?

Answer & Explanation

Sariah Glover

Sariah Glover

Beginner2022-07-05Added 16 answers

x 2 x = 3 x x 2 = 3 x x ( x 3 ) = 2 x ( x 3 ) 2 = 2 ( x 2 ) ( x 2 4 x + 1 ) = 0
Note that x = 2 is not a solution, so
x 2 4 x + 1 = 0 x = 2 + 3  or  x = 2 3
The second is not a solution either, so x = 2 + 3 .
The second is not a solution either, so x = 2 + 3 .
In that case, x 2 x = 2 + 3 2 ( 2 + 3 ) = 2 + 3 ( 3 + 1 ) 2 = 1.
Kristen Stokes

Kristen Stokes

Beginner2022-07-06Added 2 answers

Let x 2 = y x = 2 y 2
2 y 2 1 y = 3 2 y 3 3 y 1 = 0
Let x 2 x = 2 y 2 2 y = 2 a , y 2 y a = 0         ( 1 )
2 y 1 y = 3 2 a 2 y 2 + ( 2 a 3 ) y 1 = 0         ( 2 )
(1),(2) will represent the same equation iff
1 2 = 1 2 a 3 = a 1

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