Question

If ax +by =p and bx-ay =q and a²+b²=1 then prove that p²+q²=x²+y²​

Answer 1

Answer:

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Step-by-step explanation:

The options are complex hence use of option method will not be convenient. Elimination method will be better here.

For finding value of x, the terms of y is to be eliminated by multiplying each question with exchange coefficient of y i.e multiplying equation (i) by a and (ii) by b

a

2

x+aby=ap

b

2

x−aby=bq

-------------------------------

(a

2

+b

2

)x=ap+bq ⇒ x=

a

2

+b

2

ap+bq