If b = a + cp and r = ab + \(\frac{1}{2}\)cp2, express b\(^2\) in...

Mathematics

JAMB 1981

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

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Correct Answer: Option E

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