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If b = a + cp and r = ab + 12cp2, ex...

If b = a + cp and r = ab + 12cp2, express b2 in terms of a, c, r.

A.

b2 = aV + 2cr

B.

b2 = ar + 2c2r

C.

b2 = a2 = 12 cr2

D.

b2 = 12ar2 + c

E.

b2 = 2cr - a2

Correct answer is E

b = a + cp....(i)

r = ab + 12cp2.....(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 = bac

sub. for p in eqn.(ii)

r = ab + 12c(ba)2ab+b22ab+a22c

2cr = 2ab + b2 - 2ab + a2

b2 = 2cr - a2