Given that a is the smallest positive integer, b and c are rational numbers and |2+b (3a+2c)2=0, find the algebraic formula 4ab+c −A2+c+4.

Given that a is the smallest positive integer, b and c are rational numbers and |2+b (3a+2c)2=0, find the algebraic formula 4ab+c −A2+c+4.

From the known a=1,
Because |2+b (3a+2c)2=0,
So 2+b=0,3a+2c=0,
So b=-2, c=−3
2.
Set a=1, b=-2, c=−3
2 Into the original formula to obtain:4×1×(−2)+(−3
2)
−12+(−3
2)+4=−19
2
3
2=−19
3.

From the known a=1,
Because |2+b (3a+2c)2=0,
So 2+b=0,3a+2c=0,
So b=-2, c=−3
2.
Set a=1, b=-2, c=−3
2 Substitute the original formula to obtain:4×1×(−2)+(−3
2)
−12+(−3
2)+4=−19
2
3
2=−19
3.

What does the rational set include?

Rational numbers are integers and fractions. All rational numbers can be transformed into fractions.
All rational numbers constitute a set, that is, the set of rational numbers, which is represented by the bold letter Q, and some modern mathematical books are represented by the hollow letter Q. The set of rational numbers is a subset of the set of real numbers.