If $x^2+y^2 = 45 $ and x - y = 5 then what is the value of $x^3 - y^3$ ?

275

If $x^2+y^2 = 45 $

x - y = 5

then what is the value of $x^3 - y^3$

x2 + y2 = 45

x - y = 5

 We know that,

 (a - b)² = a² + b² - 2ab

a³ - b³ = (a - b)(a² + b² + ab)

So,x - y = 5

= (x - y)² = 25

= x² + y² – 2xy = 25

= 45 – 2xy = 25

= 2xy =  20

= xy =  10

x³ - y3 = (x - y)(x² + y² + xy)

= 5{45 + 10}

= 5 × 55 = 275