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If x, y, z > 0 and x ≠ 1, y ≠ 1, z ≠ 1 such that log x/y−z =log y/z−x =log z/x−ythen prove thatx^xy^y z^z = 1. |
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Answer» Answer: We have, ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣
1+x 1 1
1 1+y 1
1 1 1+z
∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ =0 ⇒ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣
x 0 1
−y y 1
0 −z 1+z
∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ =0, use R 1 →R 1 −R 2 and R 2 →R 2 −R 3
⇒x[y(1+z)+z]+y(0+z)=0 ⇒xy(1+z)+xz+yz=0 ⇒xy+yz+zx=−xyz ⇒x −1 +y −1 +z −1 =−1, divide both SIDES by xyz Step-by-step explanation: i have followed you |
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