1. If $$a^x = (x+y+z)^y$$ , $$a^y =(x+y+z)^z$$ and $$a^z = (x + y + z)^x$$ , then the value of x + y + z (given a ≠ 0) is
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By: anil on 05 May 2019 01.51 am
Expressions : $$a^x = (x+y+z)^y$$ $$a^y =(x+y+z)^z$$ $$a^z = (x + y + z)^x$$
Multiplying above equations, we get : => $$a^x imes a^y imes a^z = (x + y + z)^x imes (x + y + z)^y imes (x + y + z)^z$$ => $$(a)^{x + y + z} = (x + y + z)^{x + y + z}$$ Since the power on both sides is same, thus : => $$x + y + z = a$$
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Multiplying above equations, we get : => $$a^x imes a^y imes a^z = (x + y + z)^x imes (x + y + z)^y imes (x + y + z)^z$$ => $$(a)^{x + y + z} = (x + y + z)^{x + y + z}$$ Since the power on both sides is same, thus : => $$x + y + z = a$$