Question

The sum of two numbers is 9 and their product is 20.Find the sum of sqaures and cubes

Answer 1

The numbers are 4 & 5
(4+5= 9) & (4x5=20)

Sq. Of 4 =16
Sq. Of 5=25
Sum of sq.s =16 + 25 = 41

Cube of 4= 64
Cube of 5= 125
Sum of cubes= 64+125 = 189

Answer 2

Let the two numbers be x and y

Then

x+y=9
xy=20

Then

(x+y)²=x²+y²+2(xy)

9²=x²+y²+2*20

81=x²+y²+40

81-40=x²+y²

41=x²+y²




And





(x+y)³=x³+y³+3xy(x+y)

9³=x³+y³+3*20*9

729-540=x³+y³

189=x³+y³