What is 3-2xλ=0,-1-2yλ=0,-x^2-y^2+4=0 ?

The solution to 3-2xλ=0,-1-2yλ=0,-x^2-y^2+4=0 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3-2xλ=0,-1-2yλ=0,-x^2-y^2+4=0

3 - 2 x λ = 0, - 1 - 2 y λ = 0, - x^{2} - y^{2} + 4 = 0

(x = - \frac{3 10}{5}, y = \frac{2}{5}, λ = - \frac{5}{2 2})

Solution steps

3 - 2 x λ = 0 - 1 - 2 y λ = 0 - x^{2} - y^{2} + 4 = 0

Isolate

x

for

3 - 2 x λ = 0 : x = \frac{3}{2 λ}; λ \neq = 0

Plug

x = \frac{3}{2 λ}

into

- x^{2} - y^{2} + 4 = 0

- (\frac{3}{2 λ})^{2} - y^{2} + 4 = 0

Simplify

- \frac{9}{4 λ ^{2}} - y^{2} + 4 = 0

Solve the system of equations:

- 1 - 2 y λ = 0, - \frac{9}{4 λ ^{2}} - y^{2} + 4 = 0 : y = \frac{2}{5}, y = - \frac{2}{5}, λ = - \frac{5}{2 2} λ = \frac{5}{2 2}

Verify solutions by plugging them into the original equations

Therefore, the final solution for

3 - 2 x λ = 0, - 1 - 2 y λ = 0, - x^{2} - y^{2} + 4 = 0

(x = - \frac{3 10}{5}, y = \frac{2}{5}, λ = - \frac{5}{2 2})

- 10 x - 7 = 93

2 x (3 x - 5) = 3 (2 x^{2} - 3)

8 x + 2 + 3 x + 5 = x + 12

y, 3 x - 2 y = 10

\frac{3 x + 5}{4} - \frac{2 x - 3}{3} = 3

What is 3-2xλ=0,-1-2yλ=0,-x^2-y^2+4=0 ?
The solution to 3-2xλ=0,-1-2yλ=0,-x^2-y^2+4=0 is