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Question

Given that a(y + z) = x, b (z + x) = y , c(x + y) = z, shew that bc + ca+ ab + 2abc = 1.

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Solution

xayaz=0.....(i)bxy+bz=0....(ii)cx+cyz=0.....(iii)

Applying cross multiplicatio on (i) and (ii)

xaba=yb+ab=z1+abxa+ab=yb+ab=z1ab=kx=k(a+ab),y=k(b+ac),z=k(1ab)

substituting x,y and z in (iii)

ck(a+ab)+c(b+ab)k(1ab)=0ac+abc+bc+abc1+ab=0ab+bc+ac+2abc=1

Hence proved.


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