Question

the sum of two numbers is 9and their product is 20.find their sum of their : squares and cubes​

Answer 1

let one number be x

therefore second number will be 9-x

product of 2 numbers = 20

(x)(9-x) =20

9x-x^2=20

-x^2+9x=20

x^2-9x=-20

x^2-9x+20=0

x^2-4x-5x+20=0

x(x-4)-5(x-4) =0

(x-4)(x-5) =0

either x=4. or. x=5

9-x=9-4. 9-x=9-5

=5. =4

the sum of their square:

(x)^2+(9-x)^2. or (x)^2+(9-x)^2

=(4)^2+(5)^2. =(5)^2+(4)^2

=16+25. =25+16

=41. =41

the sum of their cube is:

(x)^3+(9-x)^3. or (x)^3+(9-x)^3

=(4)^3+(5)^3. =(5)^3+(4)^3

=64+625. =625+64

=689. =689