Question

A+b=1 a²+b²=2 a³+b³=x​

Answer 1

Ответ:

2$\frac{1}{2}$

Объяснение:

(a+b)²=a²+b²+2ab=2+2ab

2+2ab=1

ab=-1/2

Теперь

(a+b)(a²+b²)=a³+b³+ab²+a²b=a³+b³+ab(a+b)

1*2=a³+b³-1/2*1

a³+b³=2$\frac{1}{2}$

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Answer 2

To find the value of x in the equations:

1. a + b = 1
2. a² + b² = 2
3. a³ + b³ = x

You can use the following approach:

First, square equation 1 to eliminate one of the variables (either a or b):

(a + b)² = 1² a² + 2ab + b² = 1

Now, you have two equations:

1. a² + b² = 2
2. a² + 2ab + b² = 1

Subtract equation 1 from equation 2 to eliminate a² + b²:

(a² + 2ab + b²) - (a² + b²) = 1 - 2 2ab = -1

Now, solve for ab:

ab = -1/2

Now, cube equation 1:

(a + b)³ = 1³ a³ + 3a²b + 3ab² + b³ = 1

Now, plug in the values you've found:

a³ + 3a²(-1/2) + 3a(-1/2)² + b³ = 1

a³ - (3/2)a² - (3/4)a + b³ = 1

Now, use equation 2 (a² + b² = 2) to replace a² + b² with 2:

2 - (3/2)a - (3/4)a + b³ = 1

Now, simplify:

2 - (3/2)a - (3/4)a + b³ = 1

Combine like terms:

2 - (9/4)a + b³ = 1

Now, isolate b³:

b³ = 1 - 2 + (9/4)a

b³ = -1 + (9/4)a

Now, plug this expression for b³ back into equation 3:

a³ + (-1 + (9/4)a) = x

Now, simplify:

a³ - (9/4)a + 1 = x

So, the value of x in terms of a is:

x = a³ - (9/4)a + 1

This is the expression for x in terms of a. If you have a specific value of 'a,' you can substitute it into this equation to find the corresponding value of 'x.'