What is x+y=1,1xy=30 ?

The solution to x+y=1,1xy=30 is

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x+y=1,1xy=30

x + y = 1, 1 x y = 30

(x = \frac{1}{2} + i \frac{119}{2}, x = \frac{1}{2} - i \frac{119}{2}, y = \frac{1}{2} - i \frac{119}{2} y = \frac{1}{2} + i \frac{119}{2})

Solution steps

[x + y = 1 1 \cdot x y = 30]

Isolate

x

for

x + y = 1 : x = 1 - y

Plug the solutions

x = 1 - y

into

1 x y = 30

For

1 x y = 30

, subsitute

x

with

1 - y : y = \frac{1}{2} - i \frac{119}{2}, y = \frac{1}{2} + i \frac{119}{2}

Plug the solutions

y = \frac{1}{2} - i \frac{119}{2}, y = \frac{1}{2} + i \frac{119}{2}

into

x + y = 1

For

x + y = 1

, subsitute

y

with

\frac{1}{2} - i \frac{119}{2} : x = \frac{1}{2} + i \frac{119}{2}

For

x + y = 1

, subsitute

y

with

\frac{1}{2} + i \frac{119}{2} : x = \frac{1}{2} - i \frac{119}{2}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x + y = 1, 1 x y = 30

are

(x = \frac{1}{2} + i \frac{119}{2}, x = \frac{1}{2} - i \frac{119}{2}, y = \frac{1}{2} - i \frac{119}{2} y = \frac{1}{2} + i \frac{119}{2})

y - y^{2} y = x, x = 6

2 x + 3 y = 7, 3 x - 2 y = 4

x + y = 2 x y, x - y = x y

f (x) = 5, x^{2} = \frac{1}{2}

\frac{10}{( x + y )} + \frac{2}{( x - y )} = 4, \frac{15}{( x + y )} - \frac{5}{( x - y )} = - 2