Question

if x+y=5 , x^3 +y^3 = 35 find x-y

Answer 1

x+y = 5

x³+y³ = 35
=>(x+y)³-3xy(x+y) =35
=> 125 -15xy =35
=>-15xy = -90
=>xy=6

now, (x-y)² = x² + y² - 2xy
=>(x-y)² = (x+y)² -4xy
=>(x-y)²=25 -24
=>x-y = ±1

Answer 2

${x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ 35 = {5}^{3} - 3 \times xy \times 5 \\ xy = \frac{125 - 35}{15} = 6 \\ \\ {(x - y)}^{2} = {(x + y)}^{2} - 4xy \\ = {5}^{2} - 4 \times 6 = 1 \\ so \: \: x - y = \sqrt{1} = + \: or \: - 1$