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(C) Let the two numbers be $x$ and $y$.Given that the sum of the numbers is $x + y = 24$.Given that the product of the numbers is $xy = 143$.We need t

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$290$

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(C) Let the two numbers be $x$ and $y$.Given that the sum of the numbers is $x + y = 24$.Given that the product of the numbers is $xy = 143$.We need to find the sum of their squares,which is $x^2 + y^2$.Using the algebraic identity: $(x + y)^2 = x^2 + y^2 + 2xy$.Rearranging the identity to solve for $x^2 + y^2$: $x^2 + y^2 = (x + y)^2 - 2xy$.Substituting the given values: $x^2 + y^2 = (24)^2 - 2(143)$.Calculating the squares and product: $x^2 + y^2 = 576 - 286$.Therefore,$x^2 + y^2 = 290$.

The sum of two numbers is $24$ and their product is $143$. The sum of their squares is

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