{"id":4725,"date":"2022-09-01T14:04:43","date_gmt":"2022-09-01T12:04:43","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/nerovnice-priklad-1\/"},"modified":"2022-09-01T14:08:23","modified_gmt":"2022-09-01T12:08:23","slug":"nerovnice-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/nerovnice-priklad-1\/","title":{"rendered":"Nerovnice – p\u0159\u00edklad 1"},"content":{"rendered":"

Zad\u00e1n\u00ed:<\/strong> Ke ka\u017ed\u00e9 nerovnici (1-3) \u0159e\u0161en\u00e9 v oboru R<\/em><\/strong> p\u0159i\u0159a\u010fte mno\u017einu v\u0161ech \u0159e\u0161en\u00ed (a-e).
$$1. x^{2} \u2264 0$$
$$2. -2x \u2264 4-2\\cdot2$$
$$3. \\frac{2x^{2}-4x}{(x-2)\\cdot x} \u2264 0$$
 
Mno\u017einy \u0159e\u0161en\u00ed:
$$a) \u00d8$$
$$b) {0}$$
$$c) \u23290; +\u221e)$$
$$d) (-\u221e; 0\u232a$$
$$e) jin\u00e1$$<\/p>\n

\u0158e\u0161en\u00ed:<\/strong><\/p>\n

1) Zn\u00e1zorn\u011bn\u00ed nerovnice<\/p>\n

$$ x^{2} \u2264 0$$<\/p>\n

\"\"<\/p>\n

$$x^{2} \u2264 0$$ nikdy z\u00e1porn\u00fdch hodnot nenab\u00fdv\u00e1, pouze hodnoty 0, viz graf, proto je spr\u00e1vn\u011b za (b).<\/p>\n

2) Zn\u00e1zorn\u011bn\u00ed nerovnice<\/p>\n

$$ -2x \u2264 4-2\\cdot2$$<\/p>\n

\"\"<\/p>\n

Kladn\u00fdch hodnot a nuly nerovnice nab\u00fdv\u00e1 v intervalu (c).
$$-2x \u2264 4-2\\cdot2$$
V prvn\u00edm kroku si rozn\u00e1sob\u00edme pravou stranu $$-2x \u2264 0$$
P\u0159epo\u010d\u00edt\u00e1me na 1x, v\u00fdsledek v tomto p\u0159\u00edpad\u011b z\u016fst\u00e1v\u00e1 stejn\u00fd $$x \u2264 0$$<\/p>\n

3) Zn\u00e1zorn\u011bn\u00ed nerovnice<\/p>\n

$$ \\frac{2x^{2}-4x}{(x-2)\\cdot x} \u2264 0$$<\/p>\n

\"\"<\/p>\n

Nerovnice nem\u00e1 \u0159e\u0161en\u00ed, jak je patrn\u00e9 z grafu, proto je (a) spr\u00e1vn\u00e1 odpov\u011b\u010f.
$$\\frac{2x^{2}-4x}{(x-2)x} \u2264 0$$<\/p>\n

<\/p>\n

\u010casov\u00e1 n\u00e1ro\u010dnost: 7 minut<\/p>\n

Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4725","lesson","type-lesson","status-publish","hentry"],"yoast_head":"\nNerovnice - p\u0159\u00edklad 1 | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/nerovnice-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Nerovnice - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Ke ka\u017ed\u00e9 nerovnici (1-3) \u0159e\u0161en\u00e9 v oboru R p\u0159i\u0159a\u010fte mno\u017einu v\u0161ech \u0159e\u0161en\u00ed (a-e).$$1. x^{2} \u2264 0$$$$2. -2x \u2264 4-2cdot2$$$$3. frac{2x^{2}-4x}{(x-2)cdot x} \u2264 0$$  Mno\u017einy \u0159e\u0161en\u00ed:$$a) \u00d8$$$$b) {0}$$$$c) \u23290; +\u221e)$$$$d) (-\u221e; 0\u232a$$$$e) jin\u00e1$$ \u0158e\u0161en\u00ed: 1) Zn\u00e1zorn\u011bn\u00ed nerovnice $$ x^{2} \u2264 0$$ $$x^{2} \u2264 0$$ nikdy z\u00e1porn\u00fdch hodnot nenab\u00fdv\u00e1, pouze hodnoty 0, viz graf, proto je spr\u00e1vn\u011b za ... 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