The difference between two positive integers | vedclass

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Question

(B) Let the two positive integers be $x$ and $y$.Given that $x - y = 3$ and $x^2 + y^2 = 369$.We know the algebraic identity $(x - y)^2 = x^2 + y^2 -

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(B) Let the two positive integers be $x$ and $y$.Given that $x - y = 3$ and $x^2 + y^2 = 369$.We know the algebraic identity $(x - y)^2 = x^2 + y^2 - 2xy$.Substituting the known values: $3^2 = 369 - 2xy$,which gives $9 = 369 - 2xy$.Therefore,$2xy = 369 - 9 = 360$.We need to find the sum of the numbers,i.e.,$(x + y)$.Using the identity $(x + y)^2 = x^2 + y^2 + 2xy$,we substitute the values:$(x + y)^2 = 369 + 360 = 729$.Taking the square root on both sides,$x + y = \sqrt{729} = 27$ (since the integers are positive).Thus,the sum of the numbers is $27$.

The difference between two positive integers is $3$. If the sum of their squares is $369$,then the sum of the numbers is

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