Question

((а²b+b)²-b-2a²b²):a⁴=b

Answer 1

Ответ:

$({( {a}^{2}b + b) }^{2} - b - 2 {a}^{2} {b}^{2} ) \div {a}^{4} = b \\ ( {a}^{4} {b}^{2} + 2 {a}^{2} {b}^{2} + {b}^{2} - b - 2 {a}^{2} {b}^{2} ) \div {a}^{4} = b \\ {a}^{4} {b}^{2} + {b}^{2} - b = b \times {a}^{4} \\ b( {a}^{4} b + b - 1) = {a}^{4} b \\ {a}^{4}b + b - 1 = {a}^{4} \\ {a}^{4} (b - 1) + b - 1 = 0 \\ ( {a}^{4} + 1)(b - 1) = 0 \\ \\ {a}^{4} + 1 = 0 \\ b - 1 = 0 \\ \\ {a}^{4} = - 1 \\ b= 1 \\ \\ a \: є \: ∅ \\ b = 1$

Answer 2

To solve the equation ((a²b+b)²-b-2a²b²)/a⁴ = b for the variable 'a', you can follow these steps:

1. Start by simplifying the left side of the equation by expanding the square:

((a²b+b)² - b - 2a²b²) / a⁴ = b

(a⁴b² + 2ab² + b² - b - 2a²b²) / a⁴ = b

2. Now, get rid of the fractions by multiplying both sides of the equation by a⁴:

a⁴b² + 2ab² + b² - b - 2a²b² = a⁴b

3. Move all the terms involving 'a' to one side of the equation and the constants to the other side:

a⁴b² - 2a²b² + 2ab² = a⁴b - b - b²

4. Combine like terms:

a⁴b² - 2a²b² + 2ab² = a⁴b - b(1 + b)

5. Factor out the common terms:

b²(a⁴ - 2a² + 2) = a⁴b - b(1 + b)

6. Now, isolate 'a' by dividing both sides by (a⁴ - 2a² + 2):

b² = (a⁴b - b(1 + b))/(a⁴ - 2a² + 2)

7. Finally, solve for 'a'. You may need to use numerical methods or a computer algebra system to solve for 'a' because this equation appears to be a higher-degree polynomial equation and may not have simple algebraic solutions.