Cho hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iaadIhadaahaaWcbeqaaiaaiodaaaGccqGHsislcaaIYaGaamiE % aiabgUcaRiaaigdaaaa!3E2B! y = {x^3} - 2x + 1\). Tìm tất cả các điểm Mthuộc đồ thị hàm số sao cho khoảng cách từ M đến trục tung bằng 1.
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Lời giải:
Báo saiTa có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytamaabm % aabaGaamiEamaaBaaaleaacaWGnbaabeaakiaacYcacaWG5bWaaSba % aSqaaiaad2eaaeqaaaGccaGLOaGaayzkaaaaaa!3D09! M\left( {{x_M},{y_M}} \right)\) với \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa % aaleaacaWGnbaabeaakiabg2da9iaadIhadaqhaaWcbaGaamytaaqa % aiaaiodaaaGccqGHsislcaaIYaGaamiEamaaBaaaleaacaWGnbaabe % aakiabgUcaRiaaigdacaGGUaaaaa!41BF! {y_M} = x_M^3 - 2{x_M} + 1.\)
Nên \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaabm % aabaGaamytaiaacYcacaWGpbGaamyEaaGaayjkaiaawMcaaiabg2da % 9maaemaabaGaamiEamaaBaaaleaacaWGnbaabeaaaOGaay5bSlaawI % a7aiabg2da9iaaigdacqGHuhY2daWabaabaeqabaGaamiEamaaBaaa % leaacaWGnbaabeaakiabg2da9iaaigdacaaMc8UaaGPaVlaaykW7ca % aMc8UaaGPaVlablAAiHjaadMhadaWgaaWcbaGaamytaaqabaGccqGH % 9aqpcaaIWaaabaGaamiEamaaBaaaleaacaWGnbaabeaakiabg2da9i % abgkHiTiaaigdacqWIMgsycaWG5bWaaSbaaSqaaiaad2eaaeqaaOGa % eyypa0JaaGOmaaaacaGLBbaacaGGUaaaaa!62E7! d\left( {M,Oy} \right) = \left| {{x_M}} \right| = 1 \Leftrightarrow \left[ \begin{array}{l} {x_M} = 1\,\,\,\,\, \mapsto {y_M} = 0\\ {x_M} = - 1 \mapsto {y_M} = 2 \end{array} \right..\)
Vậy M(1;0) hoặc M(-1;2) .