Question

if ax + by = 3, bx - ay = 4, x^2 + y^2 = 1, then find the value of a^2 + b^2.

Answer 1

ax + by = 3 ----(1)
take square both sides ,
a²x² +b²y² +2abxy = 9

bx -ay = 4 ------------(2)
take square both sides ,
b²x² +a²y² -2abxy = 16

add equation (1) and (2)

x²(a² +b²) +y²( a²+b² ) = 9 +16
(x² +y²)(a² +b²) = 25
from question ,
x² + y² = 1
so,
a² + b² = 25

Answer 2

hey Mate here is yur answer