If xa = yb = zc and y2 = xz, find the value of b.1. (2ac)/(c + a)2. (2

1.	If xa = yb = zc and y2 = xz, find the value of b.1. (2ac)/(c + a)2. (2bc)/(b + a)3. (3ac)/(c + a)4. (3bc)/(b + c)
Answer» Correct Answer - Option 1 : (2ac)/(c + a) Given∶ x^a = y^b = z^c, y² = xz Formula Used∶ ^m√a = (a)^1/m, (a^m× aⁿ) = a^{m + n} Calculation∶ Let x^a = y^b = z^c = k, then x = k^1/a, y = k^1/b, z = k^1/c Also, y² = xz (k^1/b)² = k^1/a × k^1/c = k1^/a+1/c k^(c+a)/ac K^2/b = k^(c+a)/ac Or 2/b = (c + a)/ac 2 × ac = b × (c + a) ∴ The value of b is (2ac)/(c + a).

If xa = yb = zc and y2 = xz, find the value of b.1. (2ac)/(c + a)2. (2bc)/(b + a)3. (3ac)/(c + a)4. (3bc)/(b + c)

Answer» Correct Answer - Option 1 : (2ac)/(c + a)

Given∶ x^a = y^b = z^c, y² = xz

Formula Used∶

^m√a = (a)^1/m, (a^m× aⁿ) = a^{m + n}

Calculation∶

Let x^a = y^b = z^c = k, then

x = k^1/a, y = k^1/b, z = k^1/c

Also, y² = xz

(k^1/b)² = k^1/a × k^1/c = k1^/a+1/c k^(c+a)/ac

K^2/b = k^(c+a)/ac

Or 2/b = (c + a)/ac

2 × ac = b × (c + a)

∴ The value of b is (2ac)/(c + a).