Question

What is the value of 3√3+√3?​

Answer 1

Answer:

math]x=\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}[/math]

[math]x^2=3+\sqrt{3+\sqrt{3+\cdots}}[/math]

[math]x^2-3=\sqrt{3+\sqrt{3+\cdots}}[/math]

[math]x^2-3=x[/math]

[math]x^2-x-3=0[/math]

[math]x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(1)(-3)}}{2(1)}[/math]

[math]x=\dfrac{1\pm\sqrt{1+12}}{2}[/math]

[math]x=\dfrac{1\pm\sqrt{13}}{2}[/math]

Answer 2

Step-by-step explanation:

please look at the above image for your answer