Question

A-b=2, ab=8a^2+b^2=? ​

Answer 1

Ответ:

Объяснение:

а-b = 2,   b = a - 2

ab=8      a(a - 2) = 8

a² - 2a - 8 = 0

a1 = 4,       a2 = -2

b1 = 2,      b2 = -4

1 вариант:  a² + b² = 4² + 2² = 20

2 вариант:  a² + b² = (-2)² + (-4)² = 20

Answer 2

To find the value of ab when a - b = 2, we can use the information provided and manipulate the equations:

1. Given: a - b = 2
2. Square both sides of this equation to get (a - b)^2 = 4.

Now, let's find the value of ab:

3. Given: ab = 8

To find ab in terms of a and b, we can use the following identity:

ab = [(a + b)^2 - (a^2 + b^2)]/2

4. Substitute the values from step 2 and step 3 into the formula:

ab = [(a + b)^2 - (a^2 + b^2)]/2

5. Plug in the known value of a - b = 2 into the equation:

ab = [(2)^2 - (a^2 + b^2)]/2

6. Simplify the equation:

ab = [4 - (a^2 + b^2)]/2

Now, we have an expression for ab in terms of a and b, but we need to find a^2 + b^2. To do that, let's rearrange the equation in terms of a^2 + b^2:

a^2 + b^2 = 4 - 2ab

Now, we can substitute the value of ab = 8 into this equation:

a^2 + b^2 = 4 - 2(8)

a^2 + b^2 = 4 - 16

a^2 + b^2 = -12

So, a^2 + b^2 = -12.