What is x+y=2,x^5+y^5=82 ?

The solution to x+y=2,x^5+y^5=82 is

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x+y=2,x^5+y^5=82

x + y = 2, x^{5} + y^{5} = 82

(x = 2.41421 \dots, x = - 0.41421 \dots, y = - 0.41421 \dots y = 2.41421 \dots)

Solution steps

[x + y = 2 x^{5} + y^{5} = 82]

Isolate

x

for

x + y = 2 : x = 2 - y

Plug the solutions

x = 2 - y

into

x^{5} + y^{5} = 82

For

x^{5} + y^{5} = 82

, subsitute

x

with

2 - y : y \approx - 0.41421 \dots, y \approx 2.41421 \dots

Plug the solutions

y = - 0.41421 \dots, y = 2.41421 \dots

into

x + y = 2

For

x + y = 2

, subsitute

y

with

- 0.41421 \dots : x = 2.41421 \dots

For

x + y = 2

, subsitute

y

with

2.41421 \dots : x = - 0.41421 \dots

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

x + y = 2, x^{5} + y^{5} = 82

are

(x = 2.41421 \dots, x = - 0.41421 \dots, y = - 0.41421 \dots y = 2.41421 \dots)

x + y - z = 17, 0 x + z - y = 130

3 x^{2} - 3 + y^{2} = 0, 2 x y = 0

1 x^{2} + x - 12 = 0, y^{2} - 5 y + 6 = 0

4 x y - 2 x^{2} = - 6, 6 x + 3 y = - 6

f (x) = x^{2} - 5 x + 3, f (x) = - 3