A Treatise On Elementary And Higher Algebra

Cover A Treatise On Elementary And Higher Algebra
A Treatise On Elementary And Higher Algebra
Theodore Strong
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" Given, 4aV + 4aVa? -f 4:abcPx — 9cd^a? + {(k?+ bcPf = 0, to find »." Because the equation is equivalent to {2ax -\-a(^ + icPf = dccPa^y we get (by extracting the square roots of the membeiB of this equation) 2ax + a(^ + i€P = ±SdVcxx.
Hence, we easily get a? = i and a = — 2a-t8dVo cu^ + hcP 2a — ZdVc 28. " Given, ma? — 2mx Vn = na? — mn, to find x.^ Since the equation is equivalent to (» Vmf — 2 V'm'n . 4- ?7m = (a? Vm — Vmn)* = na?^ we get (as in the last question), A/im/n X i^m — Vmn = ±xVn
...: and thence x = —7^=: r= and a?
^17171 l/m— Vwp 29. « Given, «? ±12^'«^ - f^i^^+i + i^ + ^i^^)^ + ^ V{a + 5)c = 0, to find a?." Putting -^Lt — ?^ = A and dividing by Ax. the equa- 9J* — 3a'J* tion (by transposition) is easily put under the form x H- 4 ^^^±^ = '-^p + (1 + 2^)^4^. ,hieh (accord- aJA a: 3t^A (3 — a*)A ' ^ ing to what has heretofore been shown) is such that the values of » and -4ir — *re the roots of the proposed equation.
• aoA. -a?
To find these values, we square both members of the preceding 4:cd .


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