Question

a×a+b×b=400,4a-4b=16 then find a and b?​

Answer 1

Answer :

a = 16, b = 12

Solution :

a² + b² = 400 ----- eq 1

4a - 4b = 16

a - b = 4

a = 4 + b

consider eq 1

Substitute a = 4 + b in eq 1

(4 + b)² + b² = 400

16 + b² + 8b + b² = 400

2b² + 8b + 16 = 400

b² + 4b + 8 = 200

b² + 4b - 192 = 0

b² + 16b - 12b - 192 = 0

b(b + 16) - 12(b + 16) = 0

(b + 16)(b - 12) = 0

b = -16 or b = 12

We consider positive number i.e, b = 12

a = 4 + b = 16

∴ a = 16, b = 12