Question

if x+y=11/2 and xy=5/2 find x-y and x2-y2

Answer 1

Step-by-step explanation:

$x + y = \frac{11}{2} ,xy = \frac{5}{2}$

$y = \frac{5}{2x}$

$∴x + \frac{5}{2x} = \frac{11}{2}$

$4 {x}^{2} + 10 = 22x$

$2 {x}^{2} - 11x + 5 = 0$

$2 {x}^{2} - 10x - x + 5 = 0$

$2x(x - 5) - 1(x - 5) = 0$

$(x - 5)(2x - 1) = 0$

x can be either 5 or 1/2

For x = 5, y = 1/2

x - y = 5 - 1/2 = 9/2

x² - y² = (5)² - (1/2)² = 25 - 1/4 = 99/4

For x = 1/2, y = 5

x - y = 1/2 - 5 = -9/2

x² - y² = (1/2)² - (25)² = 1/4 - 25 = -99/4