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
syms x y
s=solve(1/x-1/(2*y)==1/(2*x+y))
x1=s(1); x2=s(2);
y^2/x1^2 + x1^2/y^2
y^2/x2^2 + x2^2/y^2
simplify(y^2/x1^2 + x1^2/y^2)
simplify(y^2/x2^2 + x2^2/y^2)
first finds two solutions:
s =
y/4 - (17^(1/2)*y)/4
y/4 + (17^(1/2)*y)/4
and evaluates the formula sought:
ans =
(y/4 - (17^(1/2)*y)/4)^2/y^2 + y^2/(y/4 - (17^(1/2)*y)/4)^2
ans =
(y/4 + (17^(1/2)*y)/4)^2/y^2 + y^2/(y/4 + (17^(1/2)*y)/4)^2
and simplifies each:
ans =
9/4
ans =
9/4
The answer is 9/4.
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Posted by Charlie
on 2023-09-26 08:39:31 |
computer-assisted answer
