Question

For x € R, the number of real roots of the equation 3x² - 4|x-² 1| + x-1=0​

Answer 1

Answer:

For x € R, the number of real roots of the equation 3x² - 4|x-² 1| + x-1=0

→4

Answer 2

$\bold{ANSWER≈}$

e*x + ³x -4e²x + e* + 1 = 0

Let e* = t€ (0,00)

So equation becomes,

tt-4t+t+1-0

1²+1-4+ 1 1

+ = 0

t

et (t+1) = a Let = a. a > 0

(a² + a-2-4)=0

(a²-2) + (a-4)= 0

a² + a-6=0

a²+3a-2a-6-0

a(a + 3)-2(a + 3) = 0

(a + 3)(a − 2) = 0

a = 2,-3

So, a=2, a -3[. a>0]

ex + e* = 2

e²x - 2e + 1 = 0

ex=1

..x = 0 only solution.

only one real Root.