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

b² = aV + 2cr

b² = ar + 2c²r

b² = a² = \(\frac{1}{2}\) cr²

b² = \(\frac{1}{2}\)ar² + c

b² = 2cr - a²

Correct answer is E

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

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