Question

The sum of two numbers is 9and their product is 20.Find the sum of their (i) squares (ii) cubes .
​

Answer 1

Answer:

189

Step-by-step explanation:

let two numbers are a and b

(a+b)²= a²+b²+2ab

9²= a²+b²+2*20

81=a²+b²+40

81-40=a²+b²

41=a²+b²

(a+b)³= a³+b³+3ab(a+b)

9³= a³+b³+3*20(9)

729=a³+b³+540

729-540=a³+b³

189=a³+b³

Hope it helps you .....Please mark me the brainliest.....

Answer 2

Answer:

(i)41 = (x)^2 + (y)^2   and   (ii)189 =  (x)^3 + (y)^3

Step-by-step explanation:

Let the two numbers be x and y

x + y = 9 ..............................eq.1

xy = 20 ................................eq.2

According to given condition

(i) Sum of their squares i.e. (x)^2 + (y)^2

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

(9)^2 =(x)^2 + (y)^2 +2(20)

81-40 = (x)^2 + (y)^2

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

(ii)Sum of their cubes i.e. (x)^3 + (y)^3

(x+y)^3 =  (x)^3 + (y)^3 +3xy(x + y)

(9)^3 = (x)^3 + (y)^3  +3(20)(9)

729 =  (x)^3 + (y)^3  + 60(9)

729 =  (x)^3 + (y)^3  +540

729-540 = (x)^3 + (y)^3

189 =  (x)^3 + (y)^3

plz like and follow if this answer helped you.