Each of x and y is a real number that satisfies this equation:
1 1 1
--- - --- = -----
x 2y 2x+y
Determine the value of:
y2 x2
---- + ----
x2 y2
1/x - 1/2y = 1/(2x+y)
(2y-x)/(2xy) = 1/(2x+y)
(2y-x)(2x+y) = (2xy)
4xy + 2y^2 - 2x^2 - xy = 2xy
2y^2 + xy - 2x^2 = 0
u = y/x
2u^2 + u - 2 = 0
u = (-1 ± √(1+16))/2
u^2 = (1 + 17 ± 2√17) / 4
u^2 = (9 ± √17)/2
pick u^2 = (9 + √17)/2
1/u^2 = ((9 - √17)/2) / ((81-17)/4)
1/u^2 = (9 - √17)/32
u^2 + 1/u^2 = (9 + √17)/2 + (9 - √17)/32
(y/x)^2 + (x/y)^2 = (153 + 15√17)/32
approx 6.713955762
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Posted by Larry
on 2023-09-26 08:00:45 |
solution
