Question

X² +x-² = 47 ,maka nilai x½ +x-½ =

Answer 1

(x^1/2 + x^-1/2)^2 = x + x^-1 + 2

(x + x^-1)^2 + 2
= x^2 + 2 + x^-2 + 2
= x^2 + x^-2 + 4
= 47 + 4 = 51

(x + x^-1)^2 + 2 = 51
(x + x^-1)^2 = 51 - 2
(x + x^-1)^2 = 49
x + x^-1 = √49 = 7

(x^1/2 + x^-1/2)^2 = 7 + 2
(x^1/2 + x^-1/2)^2 = 9
x^1/2 + x^-1/2 = √9 = 3



maka nilai x^1/2 + x^-1/2 = 3