Answer:
a² + b² = 25/2
Step-by-step explanation:
a² – b² = 12.......eq(1)
(a – b)² = 9........eq(2)
From eq(2),
(a – b)² = 9
(a – b) = √9
(a – b) = 3.........eq(3)
Making "a" subject formula in eq(3), we have
a = b + 3............eq(4)
Substituting eq(4) into eq(1)
a² – b² = 12
(b + 3)² – b² = 12
(b+3)(b+3) – b² = 12
9+3b+3b+b²–b² = 12
9 + 6b + 0 = 12
6b = 12–9
6b = 3
b = 3/6
b = 1/2
To find "a" from eq(4), when b=1/2
a = b+3
a = 1/2 + 3
a = 7/2
Therefore,
a² + b² = (7/2)² + (1/2)² = 25/2
To check if the values of "a" and "b" is correct, from eq(1) and eq(2)
a² – b² = (7/2)² – (1/2)² = 12
(a–b)² = (7/2 – 1/2)² = 9
