What is a+b=4,a^2+b^2=2 ?

The solution to a+b=4,a^2+b^2=2 is

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a+b=4,a^2+b^2=2

a + b = 4, a^{2} + b^{2} = 2

(a = 2 - 3 i, a = 2 + 3 i, b = 2 + 3 i b = 2 - 3 i)

Solution steps

[a + b = 4 a^{2} + b^{2} = 2]

Isolate

a

for

a + b = 4 : a = 4 - b

Plug the solutions

a = 4 - b

into

a^{2} + b^{2} = 2

For

a^{2} + b^{2} = 2

, subsitute

a

with

4 - b : b = 2 + 3 i, b = 2 - 3 i

Plug the solutions

b = 2 + 3 i, b = 2 - 3 i

into

a + b = 4

For

a + b = 4

, subsitute

b

with

2 + 3 i : a = 2 - 3 i

For

a + b = 4

, subsitute

b

with

2 - 3 i : a = 2 + 3 i

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

a + b = 4, a^{2} + b^{2} = 2

are

(a = 2 - 3 i, a = 2 + 3 i, b = 2 + 3 i b = 2 - 3 i)

\frac{1}{2} x + \frac{1}{3} y = 2, \frac{5}{x} - 2 y = \frac{17}{3}

x + 3 y = 1, 3 x^{2} + 3 y^{2} = 43

u + 6 = 3, v - 4 = - 2 u + v

y^{2} x + 5 y = 7, 3 x + 2 y = 5

x^{2} + 1^{2} = 25, z = 0