The product of two numbers is 45 and the sum | vedclass

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(B) Let the two numbers be $x$ and $y$.Given that the product of the numbers is $xy = 45$ and the sum of their squares is $x^2 + y^2 = 106$.We know th

Vedclass · Accepted Answer

$5$ and $9$

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(B) Let the two numbers be $x$ and $y$.Given that the product of the numbers is $xy = 45$ and the sum of their squares is $x^2 + y^2 = 106$.We know the identity $(x + y)^2 = x^2 + y^2 + 2xy$.Substituting the given values: $(x + y)^2 = 106 + 2(45) = 106 + 90 = 196$.Thus,$x + y = \sqrt{196} = 14$.We have $x + y = 14$ and $xy = 45$.These are the roots of the quadratic equation $t^2 - (x+y)t + xy = 0$,which is $t^2 - 14t + 45 = 0$.Factoring the equation: $(t - 9)(t - 5) = 0$.Therefore,the numbers are $5$ and $9$.

The product of two numbers is $45$ and the sum of their squares is $106$. The numbers are

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