The equation x+3-4x-1+x+15-8x-1=2 has
No real root
At least one real root
Exactly one root
An infinite number of real roots
Solve the equation:
The given equation is
x+3-4x-1+x+15-8x-1=2x-1-22+x-1-42=2±x-1-2±x-1-4=21
Case 1:
x-1-2+x-1-4=22x-1-6=22x-1=8x-1=4x-1=16x=17
Case 2:
-x-1-2-x-1-4=2-2x-1+6=22x-1=-4x-1=-2x-1=4x=5
For the given equation
x-1≥0x≥1
Similarly
x+3-4x-1≥0x-1-22≥0x-1≥2x-1≥4x≥5
x+15-8x-1≥0x-1-42≥0x-1≥4x-1≥16x≥17
Therefore the only possible value of x is 17.
So, it has one real root.
Hence, option B is correct.