Question

A-b=3,Ab=2Сколько будет a^2+b^2​

Answer 1

Ответ:

a - b = 3     a * b = 2

a = b + 3

(b + 3) * b = 2

b^2 + 3b - 2 = 0

D = 9 + 16 = 25

1) b = (-3 + 5) / 2 = 1

2) b = (-3 - 5) / 2 = -4

1) b = 1 => a = 4

2) b = -4 => a = -1

a^2 + b^2

1) 16 + 1 = 17

2) 1 + 16 = 17

Ответ: 17

Объяснение:

Answer 2

To find the value of a^2 + b^2, we first need to solve the given equations A - b = 3 and Ab = 2 for the values of a and b.

Let's solve the equations step by step:

1. A - b = 3
2. Ab = 2

From equation (2), we can express A in terms of b: A = 2/b

Now, substitute the value of A from equation (2) into equation (1):

2/b - b = 3

To simplify the equation, multiply both sides by b to eliminate the fraction:

2 - b^2 = 3b

Rearrange the equation to bring it into standard quadratic form:

b^2 + 3b - 2 = 0

Now, solve the quadratic equation for b using factoring or the quadratic formula:

b^2 + 3b - 2 = (b + 2)(b - 1) = 0

Setting each factor to zero:

1. b + 2 = 0 => b = -2
2. b - 1 = 0 => b = 1

Now that we have two possible values for b, we can find the corresponding values for A:

1. b = -2 => A = 2/(-2) = -1
2. b = 1 => A = 2/1 = 2

Now, we have two pairs of values for a and b:

1. a = -1, b = -2
2. a = 2, b = 1

Finally, we can calculate a^2 + b^2 for both pairs:

1. (-1)^2 + (-2)^2 = 1 + 4 = 5
2. 2^2 + 1^2 = 4 + 1 = 5

So, regardless of the values of a and b, a^2 + b^2 will always be equal to 5.