If b = a + cp and r = ab + (frac{1}{2})cp2, express b2 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
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