The product of two numbers is 120 and the sum | vedclass

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Question

(B) Let the two numbers be $x$ and $y$.Given that the product of the numbers is $x y = 120$.Given that the sum of their squares is $x^2 + y^2 = 289$.W

Vedclass · Accepted Answer

$23$

Vedclass · Answer

(B) Let the two numbers be $x$ and $y$.Given that the product of the numbers is $x y = 120$.Given that the sum of their squares is $x^2 + y^2 = 289$.We know the algebraic identity $(x + y)^2 = x^2 + y^2 + 2xy$.Substituting the given values into the identity:$(x + y)^2 = 289 + 2(120)$$(x + y)^2 = 289 + 240$$(x + y)^2 = 529$Taking the square root on both sides,we get $x + y = \sqrt{529} = 23$.Therefore,the sum of the numbers is $23$.

The product of two numbers is $120$ and the sum of their squares is $289$. The sum of the numbers is

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