Find real numbers a and b such that the equation is true.

Question

Find real numbers a and b such that the equation  is true.

Quizplus · Accepted Answer

Let's first try to simplify the given equation:
$\sqrt{(a^2 - b)^2} = a^2 - 2ab + b^2 - a + b + 1 \$
Simplifying inside the square root:
$|a^2 - b| = (a - b)^2 - a + b + 1 \$
Now, we can plug in some values and eliminate options. Let's try $a=2$ and $b=1$. 
$|2^2 - 1| = (2 - 1)^2 - 2 + 1 + 1 = 1 \$
So, we need an option where the absolute value of $a^2-b$ is 1. 
Option D satisfies this condition: $|8-5|=3=(9-16)+8-5+1$

Find Real Numbers a and B Such That the Equation