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Identity (x+y)(x-y)

If a x+b y=3,...

Question

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

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Solution

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

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

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

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