Question

Известно, что a - b = 10, ab = 7. Найти (a + b)^2.​

Answer 1

Ответ:

(a+b) ^2=(a+d) (a+b) =a^2+ab+ab+b^2=a^2+7+7+b^2=a^2+14+b^2

Answer 2

To find the value of (a + b)^2, we can first expand it using the formula for squaring a binomial:

(a + b)^2 = a^2 + 2ab + b^2

Given that a - b = 10 and ab = 7, we can make some substitutions to find the value of (a + b)^2.

First, let's solve for a and b individually using the given equations:

From a - b = 10, we can rearrange it to get a = b + 10.

Now, substitute this value of a into the equation ab = 7:

(b + 10)b = 7 b^2 + 10b - 7 = 0

Now, we can solve this quadratic equation for b using the quadratic formula:

b = (-10 ± √(10^2 - 4 * 1 * (-7))) / (2 * 1) b = (-10 ± √(100 + 28)) / 2 b = (-10 ± √128) / 2 b = (-10 ± 8√2) / 2 b = -5 ± 4√2

So, we have two possible values for b: b = -5 + 4√2 and b = -5 - 4√2.

Now, we can substitute these values of b back into the equation a = b + 10 to find the corresponding values of a:

For b = -5 + 4√2: a = (-5 + 4√2) + 10 a = 5 + 4√2

For b = -5 - 4√2: a = (-5 - 4√2) + 10 a = 5 - 4√2

Now that we have the values of a and b, we can substitute them into the equation (a + b)^2 = a^2 + 2ab + b^2:

For b = -5 + 4√2: (a + b)^2 = (5 + 4√2)^2 = 25 + 40√2 + 32 = 57 + 40√2

For b = -5 - 4√2: (a + b)^2 = (5 - 4√2)^2 = 25 - 40√2 + 32 = 57 - 40√2

Therefore, the value of (a + b)^2 is either 57 + 40√2 or 57 - 40√2, depending on the values of a and b.