Home » » Make K the subject of the relation T = $$\sqrt{\frac{TK - H}{K - H}}$$

# Make K the subject of the relation T = $$\sqrt{\frac{TK - H}{K - H}}$$

### Question

Make K the subject of the relation T = $$\sqrt{\frac{TK - H}{K - H}}$$

### Options

A) K = $$\frac{H(T^2 - 1)}{T^2 - T}$$

B) K = $$\frac{HT}{(T - 1)^2}$$

C) K = $$\frac{H(T^2 + 1)}{T}$$

D) K = $$\frac{H(T - 1)}{T}$$

### Explanation:

T = $$\sqrt{\frac{TK - H}{K - H}}$$

Taking the square of both sides, give

T2 = $$\frac{TK - H}{K - H}$$

T2(K - H) = TK - H

T2K - T2H = TK - H

T2K - TK = T2H - H

K(T2 - T) = H(T2 - 1)

K = $$\frac{H(T^2 - 1)}{T^2 - T}$$

## Dicussion (1)

• T = $$\sqrt{\frac{TK - H}{K - H}}$$

Taking the square of both sides, give

T2 = $$\frac{TK - H}{K - H}$$

T2(K - H) = TK - H

T2K - T2H = TK - H

T2K - TK = T2H - H

K(T2 - T) = H(T2 - 1)

K = $$\frac{H(T^2 - 1)}{T^2 - T}$$