Question

x/a + y/b=a+b………!
X/a^2+y/b^2=2

Answer 1

There is a typing mistake in the given question.

Given   a /x  + b/y  = a+b    --(1)    and   a/x²  + b/y² = 2    ---(2)
To solve for x and y.

Let 1/x = X and 1/y = Y.
Then    a X  + b Y = a+b   ---(3)
       =>  X = (a+b - bY)/a   ---(4)

            a X² + b Y² = 2     ---(5)

Substitute X from (4) in (5) and simplify.
         a  [(a+b) - bY]²/a² + b Y² = 2
        b(b+a) Y² - 2 b(a+b)Y + (a+b)²-2a = 0 
        
        Y = [ b(a+b)  + √ {b(a+b) × {b(a+b) - (b+a)² + 2a } } ]/ { b(b+a)}
           =   1  + √{a(2-a-b)} / √{b(a+b) } 
        y = 1/Y = √b(a+b) / [ √(ab+b²) + √(a (2-a-b)) ]

Substituting this value in (1) we get: 
        x = √(ab(a+b)) / [ √(ab(a+b))  -+ √(a(2-a-b))

Answer 2

Answer:

Step-by-step explanation: