Home » » If b = a + cp and r = ab + $$\frac{1}{2}$$cp2, express b2 in terms of a, c, r....

# If b = a + cp and r = ab + $$\frac{1}{2}$$cp2, express b2 in terms of a, c, r....

### Question

If b = a + cp and r = ab + $$\frac{1}{2}$$cp2, express b2 in terms of a, c, r.

### Options

A) b2 = aV + 2cr

B) b2 = ar + 2c2r

C) b2 = a2 = $$\frac{1}{2}$$ cr2

D) b2 = $$\frac{1}{2}$$ar2 + c

E) b2 = 2cr - a2

### Explanation:

b = a + cp....(i)
r = ab + $$\frac{1}{2}$$cp2.....(ii)
expressing b2 in terms of a, c, r, we shall first eliminate p which should not appear in our answer from eqn, (i)
b - a = cp = $$\frac{b - a}{c}$$
sub. for p in eqn.(ii)
r = ab + $$\frac{1}{2}$$c$$\frac{(b - a)^2}{\frac{ab + b^2 - 2ab + a^2}{2c}}$$
2cr = 2ab + b2 - 2ab + a2
b2 = 2cr - a2

## Dicussion (1)

• b = a + cp....(i)
r = ab + $$\frac{1}{2}$$cp2.....(ii)
expressing b2 in terms of a, c, r, we shall first eliminate p which should not appear in our answer from eqn, (i)
b - a = cp = $$\frac{b - a}{c}$$
sub. for p in eqn.(ii)
r = ab + $$\frac{1}{2}$$c$$\frac{(b - a)^2}{\frac{ab + b^2 - 2ab + a^2}{2c}}$$
2cr = 2ab + b2 - 2ab + a2
b2 = 2cr - a2