(√(6+(√(6+(√(6+(√(6+(√6)))))))))
SOLUTION
let x = (√(6+(√(6+(√(6+(√(6+(√6)))))))))
therefore..
x^(2 ) = 6+(√(6+(√(6+(√(6+(√(6 ))))))))
the equation is a continuos funtion
Thus
x^2 = 6+(√(6+(√(6+(√(6+(√(6+(√6) ))))))))......
since x = (√(6+(√(6+(√(6+(√(6+(√6)))))))))
Therdfore
x^2 = 6 + x
x^2 − x − 6 = 0
x^2 − 3x + 2x − 6 = 0
(x^2 − 3x) + (2x − 6) = 0
x(x − 3) + 2(x − 3) = 0
(x − 3)(x + 2) = 0
x − 3 = 0 or x − 2 = 0
x = 3 or x = −2
since negative is not allowed
Thus
x = 6
Meaning that
(√(6+(√(6+(√(6+(√(6+(√(6 )))))))))) = 3
DONE
THANK YOU SO MUCH. I UNDERSTAND THE SOLUTION.
Let z=Ax^2 +Bxy+Cy^2 . Find conditions
on the constants A,B,C that ensure
that the point (0,0,0) is a
(i) local minimum,
(ii) local maximum,
(ii) saddle point.