Please tell me the answer
Answers
EXPLANATION.
Method = 1.
⇒ √(a² + b² + 2ab) = 4.
⇒ b = 2.
As we know that,
Squaring both sides of the equation, we get.
⇒ (√(a² + b² + 2ab))² = (4)².
⇒ a² + b² + 2ab = 16.
Put the value of b = 2 in the equation, we get.
⇒ a² + (2)² + 2(a)(2) = 16.
⇒ a² + 4 + 4a = 16.
⇒ a² + 4a + 4 - 16 = 0.
⇒ a² + 4a - 12 = 0.
Factorizes the equation into middle term splits, we get.
⇒ a² + 6a - 2a - 12 = 0.
⇒ a(a + 6) - 2(a + 6) = 0.
⇒ (a - 2)(a + 6) = 0.
⇒ a = 2 and a = - 6.
Method = 2.
√(a² + b² + 2ab) = 4.
As we know that,
Formula of :
⇒ (x + y)² = x² + y² + 2xy.
Using this formula in the equation, we get.
⇒ √(a + b)² = 4.
⇒ a + b = 4.
Put the value of b = 2 in the equation, we get.
⇒ a + 2 = 4.
⇒ a = 4 - 2.
⇒ a = 2.
Answer:
The answer to this would be 2.
As a^2+b^2+2ab would be equal to 16 ( removing square root
Now if we put values of b in equation
a^2+4+2a+4 = 16
a^2+2a = 8
If we observe the equation we can see that only value that satisfies it is 2 .
Verification
a^2+2a = 8
Putting value of a
4+4= 8
8=8