Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if 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.
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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 (x+y)(x^2-xy+y^2)=x^3+y^3 and given details, we have to find the sum of two numbers.
Since, given that the product of the numbers is 10 that is xy=10
Also, given the sum of the squares of the numbers is 29 that is x^2+y^2=29
and the sum of the cubes of the numbers is 133 that is x^3+y^3=133
Using, the given identity (x+y)(x^2-xy+y^2)=x^3+y^3,
Substitute, the given values, we have,
(x+y)(29-10)=133
Simplify , we get,
(x+y)(19)=133
Divide both side by 19, we have,
(x+y)=7
Thus, the sum of two numbers is 7.
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