Question

If √a x - √b y = b - a and √b x - √a y = 0, then the value of xy is

Answer 1

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Answer 2

If √ax-√by=b-a and √bx-√ay=0 then value of xy is √ab

Given : √ax-√by=b-a , √bx-√ay=0

To Find : Value of x and y

Solution :

√a x-√b y = b - a   Eq1

√b x-√a y = 0    Eq2

Eq1 - Eq12

=> x(√a - √b)  - y(√b - √a) = b - a

=> x(√a - √b)  + y(√a - √b) = b - a

=> (x + y) (√a - √b)  = b - a

=>  (x + y) (√a - √b)  = (√b + √a)(√b - √a)

=>  (x + y) = - (√b + √a)

=>  (x + y) = - (√a + √b)   Eq3

Similarly

Eq1 + Eq2

=> x(√a + √b) -  y(√a + √b)  =  (√b + √a)(√b - √a)

=> x - y = √b - √a    Eq4

Eq3 + Eq4

=> 2x = -2√a

=> x = - √a

and y = - √b

=> xy = - √a * ( - √b) = √ab

Final answer is xy =  √ab

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