If xyz = xy.za = x.yzb = 0.xyzc, then which of the following is correct?
Explanation:
Given, xyz = xy.za = x.yzb = 0.xyzc
xyz = xy.za ⇒ xy.z = xyz1/a ⇒ xyz×0.1 = xyz1/a ...(1) ⇒ 0.1 = xyz1a-1 ...(1)
xyz = x.yzb ⇒ x.yz = xyz1/b ⇒ xyz×0.01 = xyz1/b ⇒ 0.01 = xyz1b-1 ...(2)
xyz = 0.xyzc ⇒ 0.xyz = xyz1/c ⇒ xyz×0.001 = xyz1/c ⇒ 0.001 = xyz1c-1 ...(3)
We konw, (1) × (2) = (3)
⇒ 0.1 × 0.01 = 0.001
⇒ xyz1a-1 × xyz1b-1 = xyz1c-1
⇒ xyz1a+1b-2 = xyz1c-1
⇒ 1a + 1b - 2 = 1c - 1
⇒ 1a + 1b = 1c + 1
Hence, option (a)
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