If b = a + cp and r = ab + \(\frac{1}{2}\)cp2, express b\(^2\) in terms of a, c, r.
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
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32597)