What is 3x^2+3y^2=7,x^3+y^3=3 ?

The solution to 3x^2+3y^2=7,x^3+y^3=3 is

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Popular >

3x^2+3y^2=7,x^3+y^3=3

Solution

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

Solution

x = \frac{7 + 33}{6}, x = \frac{6 - 1}{6}, x = \frac{6 + 1}{6}, x = - \frac{7 - 33}{6}, y = - \frac{33 - 3}{6} y = \frac{6 + 6}{6} y = \frac{- 6 + 6}{6} y = \frac{33 + 3}{6}

Solution steps

[3 x^{2} + 3 y^{2} = 7 x^{3} + y^{3} = 3]

Isolate

x

for

3 x^{2} + 3 y^{2} = 7 : x = \frac{7 - 3 y ^{2}}{3}, x = - \frac{7 - 3 y ^{2}}{3}

Plug the solutions

x = \frac{7 - 3 y ^{2}}{3}, x = - \frac{7 - 3 y ^{2}}{3}

into

x^{3} + y^{3} = 3

For

x^{3} + y^{3} = 3

, subsitute

x

with

\frac{7 - 3 y ^{2}}{3} : y = - \frac{33 - 3}{6}, y = \frac{6 + 6}{6}, y = \frac{- 6 + 6}{6}

For

x^{3} + y^{3} = 3

, subsitute

x

with

- \frac{7 - 3 y ^{2}}{3} : y = \frac{33 + 3}{6}

Plug the solutions

y = - \frac{33 - 3}{6}, y = \frac{6 + 6}{6}, y = \frac{- 6 + 6}{6}, y = \frac{33 + 3}{6}

into

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

For

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

, subsitute

y

with

- \frac{33 - 3}{6} : x = \frac{7 + 33}{6}, x = - \frac{7 + 33}{6}

For

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

, subsitute

y

with

\frac{6 + 6}{6} : x = \frac{6 - 1}{6}, x = - \frac{6 - 1}{6}

For

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

, subsitute

y

with

\frac{- 6 + 6}{6} : x = \frac{6 + 1}{6}, x = - \frac{6 + 1}{6}

For

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

, subsitute

y

with

\frac{33 + 3}{6} : x = \frac{7 - 33}{6}, x = - \frac{7 - 33}{6}

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

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

are

x = \frac{7 + 33}{6}, x = \frac{6 - 1}{6}, x = \frac{6 + 1}{6}, x = - \frac{7 - 33}{6}, y = - \frac{33 - 3}{6} y = \frac{6 + 6}{6} y = \frac{- 6 + 6}{6} y = \frac{33 + 3}{6}

Popular Examples

x^2+3x+2=0,y^2+7y+12=0

x^{2} + 3 x + 2 = 0, y^{2} + 7 y + 12 = 0

4x=8,x-y=6

4 x = 8, x - y = 6

8x+y=13,8x+y=13

8 x + y = 13, 8 x + y = 13

2x-y=-5,2x-y=-3

2 x - y = - 5, 2 x - y = - 3

x-y+z=2,x+3y+z=0

x - y + z = 2, x + 3 y + z = 0

Frequently Asked Questions (FAQ)

What is 3x^2+3y^2=7,x^3+y^3=3 ?
The solution to 3x^2+3y^2=7,x^3+y^3=3 is