If 2x+2/x=3, what is the value of x2+1/x2?
Show answer & explanation
Correct answer: A
Explanation
Given:
2x + 2/x = 3
According to the formula:
(x + 1/x)² = x² + 1/x² + 2
2x + 2/x = 3
2(x + 1/x) = 3
x + 1/x = 3/2
Now, squaring both sides:
(x + 1/x)² = (3/2)² = 9/4
According to the formula:
x² + 1/x² + 2 = 9/4
x² + 1/x² = 9/4 − 2
= 9/4 − 8/4
= 1/4