ax + by = 1 bx …
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Poulami Dasgupta 6 years, 10 months ago
ax+by=1...........(i)
bx+ay=(a+b)2/a2+b2..........(ii)
multiplying equation (i) by 'b' and equation (ii) by 'a'
abx+b2y=b...........(iii)
abx+a2y=a(a+b)2/a2+b2.......(iv)
subtracting(iv) from (iii) we get,
b2y-a2y=b-a(a+b)2/a2+b2
y(b2-a2)=b(a2+b2)-a(a+b)2/a2+b2
y(b2-a2)=a2b+b3-[a(a2+2ab+b2]/a2+b2
y(b2-a2)=a2b+b3-a3-2a2b-ab2/a2+b2
y(b2-a2)=b3-a3-a2b-ab2/a2+b2
y(b2-a2)=(b3-a3)-ab(a+b)/a2+b2
y(b+a)(b-a)=(b-a)(b2+ab+a2)/a2+b2
y=(b2+ab+a2)/(a2+b2)(b+a)
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