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प्रश्न
If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0
उत्तर
Let `root(x)("a") = root(y)("b") = root(z)("c")`
⇒ `"a"^(1/x) = "k", "b"^(1/y) = "k", "c"^(1/z) = "k"`
⇒ a = k, b = k, c = k
It is also given that abc = 1
⇒ kx x ky x kz = 1
⇒ `"k"^(x + y + z)` = k°
⇒ x + y + z = 0.
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