Question

A-b=8, ab=-3. Знайти (a+b) ^2

Answer 1

Сперва (а+б)²=а²+2аб+б²

теперь а-б=8 возведем в квадрат⇒
а²-2аб+б²=64
а²+б²=64+2аб   аб мы знаем⇒-3
а²+б²=64+2*(-3)=64-6=58

подставляем в  а²+2аб+б²
58+2*(-3)=58-6=52
значит (а+б)²=√52

Answer 2

$\mathtt{(a+b)^2=(a-b)^2+4ab=8^2+4*(-3)=64-12=52}$

Answer 3

To find the value of (a + b) ^ 2, we can use the identity (a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2. Given that A - b = 8 and ab = -3, we can calculate (a + b) ^ 2 as follows:

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

Now, let's find the values of a ^ 2 and b ^ 2:

a ^ 2 = (A - b) ^ 2 a ^ 2 = (8) ^ 2 a ^ 2 = 64

b ^ 2 = (ab) ^ 2 b ^ 2 = (-3) ^ 2 b ^ 2 = 9

Next, let's find the value of 2ab:

2ab = 2 * (-3) = -6

Now, plug in the values into the equation for (a + b) ^ 2:

(a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2 (a + b) ^ 2 = 64 + (-6) + 9 (a + b) ^ 2 = 64 - 6 + 9 (a + b) ^ 2 = 67

So, (a + b) ^ 2 = 67.