Given:
xy = 35
x + y = 12
To find x² + y²:
(x + y)² = x² + 2xy + y²
144 = x² + 2(35) + y²
144 = x² + 70 + y²
x² + y² = 144 - 70
= 74
Initial value = 80
Final value = 80
Percentage increase = ((Final - Initial) / Initial) × 100
= ((80 - 80) / 80) × 100
= (0 / 80) × 100
= 0%
Given x + 1/x = 3
To find x³ + 1/x³:
(x + 1/x)³ = x³ + 3(x²)(1/x) + 3(x)(1/x)² + 1/x³
= x³ + 3x + 3/x + 1/x³
= x³ + 1/x³ + 3(x + 1/x)
(x + 1/x)³ = x³ + 1/x³ + 3(3)
27 = x³ + 1/x³ + 9
x³ + 1/x³ = 27 - 9
= 18