Answer:
5/2
Explanation:
substitute the values into the cosine rule:
(2
)² = ((2x - 1)² + (2x + 1)²) - 2(2x - 1)(2x + 1)cos(60))
work out each part separately:
(2
)² = 28
(2x - 1)² = 4x² - 4x + 1
(2x + 1)² = 4x² + 4x + 1
(2x - 1)² + (2x + 1)² = (4x² - 4x + 1) + (4x² + 4x + 1) = 8x² + 2
2((2x - 1)(2x + 1)cos(60)):
(2x - 1)(2x + 1) = 4x² - 1
cos(60) = √1/2 = 1/2
2(4x² - 1)(1/2) = 4x² - 1
substitute back in:
28 = (8x² + 2) - (4x² - 1)
28 = 4x² + 3
25 = 4x²
25/4 = x²
x = √(25/4)
x = 5/2