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Q. Assertion–Reason Type Question
Statement-1: If \( a^x = b^y = c^z = abc \), then \( xy + yz + zx + xyz = 1 \)
Statement-2: If \( a^n = k \), then \( a = k^{1/n} \)
✏️ Solution
Let \( a^x = b^y = c^z = abc = k \)
Then \( a = k^{1/x},\ b = k^{1/y},\ c = k^{1/z} \)
\( abc = k^{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}} \)
But \( abc = k \)
So \( \frac{1}{x}+\frac{1}{y}+\frac{1}{z} = 1 \)
Multiply by \( xyz \)
\( xy + yz + zx = xyz \)
\( xy + yz + zx + xyz = 2xyz \neq 1 \)
So Statement-1 is FALSE
Statement-2 is TRUE
Correct Option: (d)
\( \boxed{\text{(d)}} \)