O lvl EM: Indices

Question from http://www.sgforums.com/forums/2297/topics/313742

(900 -p)^½ + 4(81-p)^½ = 50

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Answer:

let y = 81 - p

thus,

(819 + y)^½ + 4y^½ = 50
(819 + y)^½ = 50 - 4y^½

square both sides

819 + y = 2500 - 400 y^½ + 16y
15y - 400y^½ +1681 = 0

Using formula,

{ -b±√(b²- 4ac) } / 2a

y^½ = 5.23 or 21.44 (reject because y >0, (81-p)^½ = y^½ => y has to be positive)

Thus,

p = 81 - y = 81 - 5.23² = 53.65

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