If X - Y = XY = 10 then find the value of X^4 + Y^4

Question

If
x, y, z are 3 non zero positive integers such that x+y+z = 8 and xy+yz+zx = 20,
then
What would be minimum possible value of x*y^2*z^2

Answer 1

(X-Y)^2 = 100
X^2 + Y^2 - 2XY=100
Therefor: X^2+Y^2=80

(X^2+Y^2)^2=6400
X^4 + Y^4 + 2 X^2 Y^2 = 6400
As : 2 X^2 Y^2 = 200
X^4 + Y^4 + 200 = 6400
Therefor:
X^4 + Y^4 = 6200

Comments

X^2 + Y^2 - 2XY=100
-2xy=-20
Therefore: X^2+Y^2=120  (not 80)

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I agree giving 14200
much neater solution graphically

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That's not the correct answer!
Crow