Answer:
The sum of two numbers is 7.
Step-by-step explanation:
Given : the product of the numbers is 10, the sum of the squares of the numbers is 29, and the sum of the cubes of the numbers is 133.
Using identity [tex](x+y)(x^2-xy+y^2)=x^3+y^3[/tex] and given details, we have to find the sum of two numbers.
Since, given that the product of the numbers is 10 that is [tex]xy=10[/tex]
Also, given the sum of the squares of the numbers is 29 that is [tex]x^2+y^2=29[/tex]
and the sum of the cubes of the numbers is 133 that is [tex]x^3+y^3=133[/tex]
Using, the given identity [tex](x+y)(x^2-xy+y^2)=x^3+y^3[/tex],
Substitute, the given values, we have,
[tex](x+y)(29-10)=133[/tex]
Simplify , we get,
[tex](x+y)(19)=133[/tex]
Divide both side by 19, we have,
[tex](x+y)=7[/tex]
Thus, the sum of two numbers is 7.
Answer:
x+y = 7
Step-by-step explanation:
We have given that
The product of the numbers is 10
xy = 10
The sum of the squares of the numbers is 29
x²+y² = 29
The sum of the cubes of the numbers is 133
x³+y³ = 133
We have to find that the sum of two numbers.
x+y = ?
Using given formula, we have
(x+y)(x²-xy+y²) = x³+y³
(x+y)(x²+y²-xy) = x³+y³
Putting given value in above formula, we have
(x+y)(29-10) = 133
(x+y)(19) = 133
(x+y) = 133 / 19
x+y = 7 which is the answer.
