# Need help to get the X-Intercept of this 2x−√x²+1 [closed]

i am a senior high school student i need getting the X-Intercept . Because my teacher told us the answer but i can not get it right . the answer is x=√3/3

• see Documentation >> Solve and try Solve[2 x - Sqrt[x^2 + 1] == 0, x]
– kglr
Oct 25, 2017 at 7:46
• Sorry i can not Oct 25, 2017 at 7:53
• Why? $\phantom{}$ Oct 25, 2017 at 7:55

 f[x_] := 2*x - Sqrt[x^2 + 1]


You can get the x-Intercept with:

sol = x /. Solve[f[x] == 0, x] // First
(*-> 1/Sqrt[3]*)


Notice that

$\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}$

Plot the result:

 Plot[f[x], {x, -1, 10},Epilog -> {Red, PointSize[0.02], Point[{sol, 0}]}]


• I really thank you. How could you do that ?? Is it a program?? Can u tell me the name? Oct 25, 2017 at 8:41
• Since you posted in the Mathematica StackExchange I used Wolfram Mathematica Oct 25, 2017 at 8:42
• How can i use it ?? Oct 25, 2017 at 8:46
• You need to purchase a license. But since you are a student your school/university maybe already did that. Oct 25, 2017 at 8:50