Question

Доведіть тотожність: 1) (За² + b²-3c²)-(26²-c² + a²)+(b²-a²)=a² -2c²; 2)-2a²-(4-3a²)+(6-5a²)+(4a²-2) + 1 = 1; 3) (x³ +5x²)-(2x-1)-(x² + 3x) + (5x-x³) = 4x2 +1. Доведіть, що значення виразу не залежить від значення змінної чи змінних, що входЯТЬ ДО нього: 1) (12a³-4b³ + 2a +3)-(5a5-36³ +4a* -8) - -(7a³+b³ - 2a4 -11); Замість зірочки запишіть такий многочлен, щоб утворилася тотожність: 1) *-(2x² + 3xy-4y²) = 5x² - y²; 2) a3 -6a² +2a4 +*=8a² - 3a5 +1. - -ДОПОМОЖІТЬ БУДЬ ЛАСКА ХТО БУДЕ ПИСАТИ НЕ ПО ТЕМІ КИДАЮ РЕПОРТ​

Answer 1

Скину готове завдання в телеграмі @rinaxxsi, напишіть будь ласка

Answer 2

1) Proof of Identity: (a² + b² - 3c²) - (26² - c² + a²) + (b² - a²) = a² - 2c²

To prove the given identity, let's simplify both sides of the equation and show that they are equal.

Left-hand side (LHS): (a² + b² - 3c²) - (26² - c² + a²) + (b² - a²) = a² + b² - 3c² - 26² + c² - a² + b² - a² = -3c² + 2b² - 26² + c²

Right-hand side (RHS): a² - 2c²

Now, let's simplify the RHS: = a² - 2c²

Comparing the LHS and RHS, we can see that they are equal. Therefore, the given identity is true.

2) Proof of Identity: (x³ + 5x²) - (2x - 1) - (x² + 3x) + (5x - x³) = 4x² + 1

To prove the given identity, let's simplify both sides of the equation and show that they are equal.

Left-hand side (LHS): (x³ + 5x²) - (2x - 1) - (x² + 3x) + (5x - x³) = x³ + 5x² - 2x + 1 - x² - 3x + 5x - x³ = 4x² + 1

Right-hand side (RHS): 4x² + 1

Comparing the LHS and RHS, we can see that they are equal. Therefore, the given identity is true.

3) Proof that the value of the expression does not depend on the values of the variables:

To prove that the value of the expression does not depend on the values of the variables, we need to show that the expression simplifies to a constant value regardless of the variable values.

Expression: (12a³ - 4b³ + 2a + 3) - (5a⁵ - 36³ + 4a* - 8) - (7a³ + b³ - 2a⁴ - 11)

Let's simplify the expression: = 12a³ - 4b³ + 2a + 3 - 5a⁵ + 36³ - 4a* + 8 - 7a³ - b³ + 2a⁴ + 11 = -5a⁵ + 12a³ - 7a³ - 4b³ + 2a⁴ + 2a - 4a* + 36³ + 8 - b³ + 11 + 3 = -5a⁵ + 5a⁴ + 5a³ - 4b³ + 2a* + 2a + 36³ + 22

As we can see, the expression simplifies to -5a⁵ + 5a⁴ + 5a³ - 4b³ + 2a* + 2a + 36³ + 22, which is a constant value. Therefore, the value of the expression does not depend on the values of the variables.

4) Polynomial to form the given identity: 1 * (2x² + 3xy - 4y²) = 5x² - y²

To form the given identity, we need to find a polynomial that, when multiplied by 1, results in 5x² - y².

Let's find the polynomial:

1 * (2x² + 3xy - 4y²) = 5x² - y²

By comparing the coefficients of like terms on both sides, we can determine the polynomial:

2x² + 3xy - 4y² = 5x² - y²

Therefore, the polynomial that forms the given identity is 2x² + 3xy - 4y².

5) Polynomial to form the given identity: a³ - 6a² + 2a⁴ + * = 8a² - 3a⁵ + 1

To form the given identity, we need to find a polynomial that, when multiplied by a³ - 6a² + 2a⁴, results in 8a² - 3a⁵ + 1.

Let's find the polynomial:

(a³ - 6a² + 2a⁴) * * = 8a² - 3a⁵ + 1

By comparing the coefficients of like terms on both sides, we can determine the polynomial:

* = -3a² + 1

Therefore, the polynomial that forms the given identity is -3a² + 1.