Question 134
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
Solution
Expressions : $$a^x = (x+y+z)^y$$
$$a^y =(x+y+z)^z$$
$$a^z = (x + y + z)^x$$
Multiplying above equations, we get :
=> $$a^x \times a^y \times a^z = (x + y + z)^x \times (x + y + z)^y \times (x + y + z)^z$$
=> $$(a)^{x + y + z} = (x + y + z)^{x + y + z}$$
Since the power on both sides is same, thus :
=> $$x + y + z = a$$
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