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MATH SOLVE for A and B (a+1)²+b²=4a+3(2b-3)?
(a+1)²+b²=4a+3(2b-3)
2 Answers
- MichaelLv 74 months ago
(a + 1)² + b² = 4a + 3(2b-3)
Expand
(a² + 2a + 1) + b² = 4a + (6b - 9)
Rearrange
a² - 2a + 1 = -b² + 6b - 9
Factor
(a - 1)² = -(b - 3)²
-------------------
Solve for a
Take the square root of both sides
a - 1= ±√(-(b - 3)² )
add 1 to both sides
a = 1 ± √( -(b - 3)² ) <–––––––
The only real solution is when
( -(b - 3)² ) = 0
all other solutions will be imaginary
therefor
b = 3
a = 1
----------------------
Solve for b
Multiply both sides of (a - 1)² = -(b - 3)² by -1
-(a - 1)² = (b - 3)²
Take the square root of both sides
±√( -(a - 1)² ) = b - 3
Add 3 to both sides
b = 3 ± √( -(a - 1)² ) <–––––––––
The only real solution is when
( -(a - 1)² ) = 0
all other solutions will be imaginary
therefor
a = 1
b = 3
