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Given that x-y =
[tex] 8\sqrt{2} [/tex]
and xy = 137,
where x and y are both positive,
find the value of x + y without finding x or y
​

Sagot :

Answer:

x + y = 26

Step-by-step explanation:

The idea is to express  (x+y)^2  via given data, and then take square root of this expression (of this number).

It will be exactly (x+y).

So,

[tex](x+y)^{2} =(x-y)+4xy=(8*\sqrt{2} )^{2} + 4*137 = 64*2 + 4*137 = 676.[/tex]

[tex]Therefore, (x+y) = \sqrt{676} =26[/tex]

Answer: [tex]x + y = 26.[/tex]

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