Question

x/a + y/b=a+b, x/a2+y/b2 = 2​

Answer 1

x / a + y / b = a + b ————— ( i )

x / a² + y / b² = 2 —————— ( ii )

equation ( i ) × 1 / a => x / a² + y / ab = ( a + b ) / a

equation ( ii ) × 1 => x / a² + y / b² = 2

( - ) ( - )

——————————————————————————

substract y / ab - y / b² = ( a + b ) / a - 2

=> ( yb - ya ) = a + b - 2a / a

=> y ( b - a ) = ( b - a ) / a

=> y = ( b - a ) / a × 1 / b - a

=> y = 1 / a

Now, y = 1 / a put in equation ( i )

x / a + 1 / a / b = a + b

=> x/ a + 1 / ab = a + b

=> bx + 1 = a + b

=> bx = a + b - 1

=> x = ( a + b - 1 ) / b

( x, y ) = { ( a + b - 1 ) / b, 1 / a }

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