Question

ax + by =6 and bx - ay = 2 and x²+y² = 4. Then find the value of (a²+b²).

Answer 1

Answer:

10

Step-by-step explanation:

Eqn  :> ax + by = 6

     Square both sides: (ax)² + (by)² + 2axby = 36 ----(1)

Eqn  :> bx - ay = 2

     Square both sides: (bx)² + (ay)² - 2axby = 4 ----(2)

Now, Add (1) and (2):

=> (ax)² + (by)² +(bx)² + (ay)² = 40

=> a²x² + b²y² + b²x² + a²y² = 40

=> x²(a²+b²) + y²(a²+b²) = 40

=> (a²+b²)(x²+y²) = 40

=> (a²+b²)(4) = 40  { Given : (x²+y²) =4 }

=> (a²+b²) = 10