Question

The sum of two numbers is 8 and their product is 15. Find the sum of their i) squares ii) cubes

Answer 1

Answer:

let the first no be x and second no be y

x+y = 8 ........(2)

xy=15

we know that

(x+y)²-(x-y)²=4xy

64-(x-y)²=4×15

(x-y)²=4

x-y=2.......(1)

form 1 and 2

2x=10

x=5

put x=5in 1

5-y=2

y=3

Step-by-step explanation:

so (x²+y²)=25+9=34

(x³+y³)=125+27=152

Answer 2

Step-by-step explanation:

Let,two numbers be x,y

Given,x+y=8,xy=15

y=8-x

x(8-x)=15

8x-x^2=15

x^2-8x+15=0

x^2-5x-3x+15=0

x(x-5)-3(x-5)=0

(x-3)(x-5)=0

x=3,5

At,x=3

y=8-3

=5

At,x=5

y=3

i)sum of their squares is

At,x=3,y=5

x^2+y^2=(3)^2+(5)^2

=9+25

=34

At,x=5,y=3

x^2+y^2=34

ii)sum of their cubes is

x^3+y^3=(3)^3+(5)^3

=27+125

=152