perplexus.info :: Just Math : Set of 2 Radical Equations

Set of 2 Radical Equations (Posted on 2024-10-23)

Given that:

A√A + B√B = 85
A√B + B√A = 86

Find the value of A+B.

No Solution Yet Submitted by K Sengupta

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Solution

Comment 1 of 1

Let x=√A any y=√B; x,y >= 0

Looking for value of x^2 + y^2

x^3 + y^3 = (x+y)(x^2 - xy + y^2) = 85

x^2y + xy^2 = (x+y)(xy) = 86

(x+y)^3 = (x^3 + y^3) + 3xy(x+y)

(x+y)^3 = 85 + 3*86 = 343 = 7^3

x+y = 7

(x^2 - xy + y^2) = 85/7

(xy) = 86/7

x^2 + y^2 = 85/7 + xy

x^2 + y^2 = 85/7 + 86/7

x^2 + y^2 = 171/7

A + B = 171/7

Posted by Larry on 2024-10-23 13:00:46

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