From the option given the value 25/16 is quite close to the solution. Hence the option B is the correct option.
We are required to find the roots of the given equation,
[tex]\dfrac{1}{2} x^3+x-7=-3\sqrt{x-1}[/tex]
Arrange the equation,
[tex]\dfrac{1}{2} x^3+x-7+3\sqrt{x-1}=0[/tex]
Rewrite the equation in a function form
[tex]f(x)=\dfrac{1}{2} x^3+x-7+3\sqrt{x-1}[/tex]
[tex]f(x)=\dfrac{1}{2} x^3+x-7+3\sqrt{x-1}[/tex]
The equation will have a solution when [tex]f(x)=0[/tex]. We'll start from the approximate crossing point given in the graph x=1.5,
[tex]f(x)=\dfrac{1}{2} 1.5^3+1.5-7+3\sqrt{1.5-1}=-1.689[/tex]
This value is closer to the solution. From the option given the value 25/16 is quite close to the solution. Hence the option B is the correct option.
For more about the graph follow the link given below-
https://brainly.com/question/14375099
