What is 2a^2=6a^3-a^6,b=1 ?

The solution to 2a^2=6a^3-a^6,b=1 is

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2a^2=6a^3-a^6,b=1

2 a^{2} = 6 a^{3} - a^{6}, b = 1

a = 0, a = 0.33544 \dots, a = 1.68869 \dots, b = 1 b = 1 b = 1

Solution steps

[2 a^{2} = 6 a^{3} - a^{6} b = 1]

Solve

2 a^{2} = 6 a^{3} - a^{6} : a = 0, a \approx 0.33544 \dots, a \approx 1.68869 \dots

For

b = 1

, subsitute

a

with

0 : b = 1

For

b = 1

, subsitute

a

with

0.33544 \dots : b = 1

For

b = 1

, subsitute

a

with

1.68869 \dots : b = 1

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

2 a^{2} = 6 a^{3} - a^{6}, b = 1

are

a = 0, a = 0.33544 \dots, a = 1.68869 \dots, b = 1 b = 1 b = 1

x + 6 y = 3, x y = - 9

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

3 x - y = 3, - 3 x + y = 3

1 y = x^{2} - 5 x + 7, y = 2 x + 1

x^{2} + y = 37, 3 x + 4 y = 22