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