Question

If x^2+ y^2=58 andx+y=10, then find the value of x^3+y^3.

Answer 1

since
(x+y)²=x²+y²+2xy,

then

10²=58+2xy,

100-58=2xy,

2xy=42,

xy=21,

therefore

x³+y³=(x+y)(x²+y²-xy),

x³+y³=10×(58-21),

x³+y³=10×37,

x³+y³=370

Answer 2

Answer:

Given

x^2+y^2=58

x+y = 10

To find

x^3+y^3 = ?

Solution:

(x+y)^2=x^2+y^2+2xy

(10)^2 = 58+2xy

100 = 58+2xy

2xy = 100 - 58

2xy = 42

xy = 42/2

xy = 21

now

x^3+y^3= (x+y)(x^2+y^2-xy)

= 10 (58 21)

= 10 X 37

x^3+y^3= 370