Question

(i) lf x = 2, y = 1 then x^x + y^y = 5.

(ii) If a = b^x, b = c^y, c = a^z then xyz = 1.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

(i) If x = 2, y = 1

Then x^x + y^y = 2² + 1¹

x^x + y^y = 4 + 1

x^x + y^y = 5

So, statement (i) is true.

(ii) If a = b^x, b = c^y, c = a^z, then by substituting and equating exponents, it can be shown that xyz = 1.

This is a known property from the exponential relationships given.

Hence, both statements (i) and (ii) are valid.