Giải toán trên máy tính Casio - THPT & THCS (Combo by Dạy Kèm Quy Nhơn Official)

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PhÇn I: C¸c bµi to¸n vÒ ®a thøc 1. TÝnh gi¸ trÞ cña biÓu thøc: Bµi 1: Cho ®a thøc P(x) = x15 -2x12 + 4x7 - 7x4 + 2x3 - 5x2 + x - 1 TÝnh P(1,25); P(4,327); P(-5,1289); P( 1 3 ) 4

H.DÉn: - LËp c«ng thøc P(x) - TÝnh gi¸ trÞ cña ®a thøc t¹i c¸c ®iÓm: dïng chøc n¨ng CALC - KÕt qu¶:

P(1,25)

=

P(-5,1289) =

; P(4,327) = ; P( 1 3 ) 4

=

Bµi 2: TÝnh gi¸ trÞ cña c¸c biÓu thøc sau: P(x) = 1 + x + x2 + x3 +...+ x8 + x9 t¹i x = 0,53241 Q(x) = x2 + x3 +...+ x8 + x9 + x10 t¹i x = -2,1345 H.DÉn: - ¸p dông h»ng ®¼ng thøc: an - bn = (a - b)(an-1 + an-2b +...+ abn-2 + bn-1). Ta cã: P(x) = 1 + x + x2 + x3 +...+ x8 + x9 =

( x − 1)(1 + x + x 2 + ... + x 9 ) x10 − 1 = x −1 x −1

Tõ ®ã tÝnh P(0,53241) = T−¬ng tù: Q(x) = x2 + x3 +...+ x8 + x9 + x10 = x2(1 + x + x2 + x3 +...+ x8) = x 2

x9 − 1 x −1

Tõ ®ã tÝnh Q(-2,1345) = Bµi 3: Cho ®a thøc P(x) = x5 + ax4 + bx3 + cx2 + dx + e. BiÕt P(1) = 1; P(2) = 4; P(3) = 9; P(4) = 16; P(5) = 25. TÝnh P(6); P(7); P(8); P(9) = ? H.DÉn: B−íc 1: §Æt Q(x) = P(x) + H(x) sao cho: + BËc H(x) nhá h¬n bËc cña P(x) + BËc cña H(x) nhá h¬n sè gi¸ trÞ ®· biÕt cña P(x), trongbµi bËc H(x) nhá h¬n 5, nghÜa lµ: Q(x) = P(x) + a1x4 + b1x3 + c1x2 + d1x + e B−íc 2: T×m a1, b1, c1, d1, e1 ®Ó Q(1) = Q(2) = Q(3) = Q(4) = Q(5) = 0, tøc lµ:

a1 + b1 + c1 + d1 + e1 + 1 = 0 16a + 8b + 4c + 2d + e + 4 = 0 1 1 1 1  1 ⇒ a1 = b1 = d1 = e1 = 0; c1 = -1 81a1 + 27b1 + 9c1 + 3d1 + e1 + 9 = 0 256a + 64b + 16c + 4d + e + 16 = 0 1 1 1 1 1  625a1 + 125b1 + 25c1 + 5d1 + e1 + 25 = 0 VËy ta cã: Q(x) = P(x) - x2

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