Question

If ax +by=3,bx-ay=4 and x^2+y^2=1 then the value of a^2+b^2 is

Answer 1

Answer:

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