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数学 高校生

この問題はなぜD1が完全平方式となればいいと言えるんですか?

重要 例題 51 2次式の因数分解 (2) (0①①①①① 4x2+7xy-2y²-5x+8y+kx,yの1次式の積に因数分解できるように, 定数kの値を定めよ。 また, そのときの因数分解の結果を求めよ。 [類 創価大〕 |基本 20,46 CHART OLUTION 2次式の因数分解 =0 とおいた2次方程式の解を利用 (与式)=0 とおいた方程式をxの2次方程式とみたとき (yを定数とみる), 判別 —(7y—5)—√D₁ 式をD, とすると、与式は4{x-(7y-5)+√D}{x-(y-5)-D} の形 8 8 に因数分解される。D1はyの2次式であり,このときの因数がx,yの1次式と なるための条件は √DIがyの1次式⇔ D1 が完全平方式 すなわち D=0 として,この2次方程式の判別式D2 が 0 となればよい。 解答 (与式)=0 とおいた方程式をxの2次方程式とみて、 4x²+(7y-5)x-(2y²-8y-k)=0 ① の判別式をDとすると まれている。これまでと同 っと D=(7y-5)2+4・4(2y²-8y-k)=81y²-198y+25-16k 与式がxとyの1次式の積に分解されるための条件は、 ①の解 がyの1次式となること,すなわち D1 がyの完全平方式とな ることである。 の D=0 とおいたの2次方程式 81y²-198y+25-16k=0 0 判別式をD2 とすると (2+8)(€ 9) = (86) D₂=(-99)²-81(25-16k)=81{11²—(25—16k)}=81(96+16k) 4 D2=0 となればよいから 96+16k = 0 よって x= ゆえに ...... このとき, D1=81y²-198y+121=(9y-11)2 であるから, ① の解は すなわち x=- , -2y+2 y-3 4 $=44-830-81 m2;&ck: __(7y-5)±√(9y-11) __(7y-5)±(9y-11) 8 8 MURDER inf. 恒等式の考えにより 解く方法もある。(解答編 および p.55 EXERCISES 15 参照 ) (5x)=4(x−y=³){x−(−2y+2)} kid =(4x-y+3)(x+2y-2) ◆ D1 が完全平方式 ⇔ 2次方程式 D1=0 が重 解をもつ =) AGOR adot 計算を工夫すると 992(9.11) 2=81112 は、 ←√(9y-11)^=|9y-11| であるが, ±がついて いるから, 9y-11の絶 対値ははずしてよい。 (括弧の前の4を忘れな - PRACTICE・・・・ 51④ を定数とする2次式 x2+3xy+2y2-3x-5y+k がx,yの1次式の積に因数分解 できるときの値を求めよ。 また, そのときの因数分解の結果を求めよ。 [東京大 2章 7 解と係数の関係

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英語 高校生

仮定法の範囲です! 6〜21、20、24〜26の答えあってるか確認して欲しいです!不正解の場合正しい回答も教えてくれると助かります🙇‍♂️

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英語 高校生

仮定法の範囲です 6〜21、20、24〜26の答え教えてください! 解いたのであってるかみてほしいです。不正解の場合正しい回答もしりたいです🙇‍♂️

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