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The sum of the squares of two positive integers is 185. If one integer is 3 less than the other, fine the larger integer.

Answer :

Alfpfeu

Answer:

[tex]\boxed{\sf \ 11 \ }[/tex]

Step-by-step explanation:

Hi,

let's note the two integers a and b

[tex]a^2+b^2=185 \ and \\\\a = b - 3[/tex]

We are asked to find b

replace a in the first equation

   [tex](b-3)^2+b^2=185\\\\<=>b^2-6b+9+b^2=185\\\\<=> 2b^2-6b+9-185=0\\\\<=> 2b^2-6b-176=0\\\\<=> b^2-3b-88=0\\\\<=>b^2+8b-11b-88=0\\\\<=>b(b+8)-11(b+8)=0\\\\<=>(b-11)(b+8)=0\\\\<=> b = 11 \ or \ b = -8[/tex]

As b must be a positive integer, the solution is 11

Hope this helps

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