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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