Question

x/a+x/b=a+b; x/a ² + y/ b ²=2
solve for x and y

Answer 1

In eq I x/a+y/b=a+b

taking LCM xb+ya/ab=a+b  eq………………………….i

subtracting a+b from eq…………. i we get

xb+ya/ab –(a+b)= (a+b)-( a+b)

xb+ya/ab-(a+b)=0

now again taking LCM we get (xb +ya –(a+b)ab)/ab   =0

xb+ya-a2b-b2a=ab  x  o  eq…………….iii

in eq2  x/a2+y/b2=2  we do same method done in eq i

then we get xb2+ya2-2a2b2 = o  x  a2b2 eq……………..iv

now multiply eq iii from  b we get xb2+bya –a2b2-b3a =0 ………. eq v

subtracting eq v from eq  iv we get

ya2-bya-a2b2-(-b3a )=0

ya2-bya=a2b2-b3a

ya(a-b)=b2a(a-b)

so  ya =b2a substituting this in eq iii we get x=a2

Answer 2

y=b², x=a ² because by multiplying 1/a both sides we get " (x/a²) +(y/ab) = 1 + (b/a) equ. 1 . and also we have given that x/a² +y/b² =2 equ . 2 and subtract 2 from 1