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If x=1+log a bc, y=1+log b ac, z=1+log c ab, Prove that xy+yz+zx = xyz answer it fassstttt
Dear student x = 1 + loga (bc)= loga (a) + loga (bc)= loga (abc)or, 1/x = log(abc) a .....(1)similarly, y = 1 + logb (ca) = logb (abc)or, 1/y = log(abc) b ......(2)and z = 1 + logc (ab) = logc (abc)or, 1/z = log(abc) c ......(3)now, 1/x + 1/y + 1/z = log(abc) a + log(abc) b + log(abc) c= log(abc) (a × b × c)= log(abc) (abc)= 1or, 1/x + 1/y + 1/z = 1or, (yz + yz + xy)/xyz = 1or, xyz = xy + yz + zxhence, xyz = xy + yz + zx
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