1.2

GRATUIT - Variantă 1 - Subiect tip 2

Caiet de clasa

TESTUL nr. 1

Subiect tip II.

1. Fie matricea , MathML (base64):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

a) Calculați detA(x)

b) Pentru x=3, determinați MathML (base64):PG1hdGg+CiAgICA8bXN1cD4KICAgICAgICA8bWk+QTwvbWk+CiAgICAgICAgPG1pPi0xPC9taT4KICAgIDwvbXN1cD4KPC9tYXRoPg==

c) Rezolvați ecuația  MathML (base64):PG1hdGg+CiAgICA8bWk+ZGV0PC9taT4KICAgIDxtaT5BKDwvbWk+CiAgICA8bXN1cD4KICAgICAgICA8bWk+MjwvbWk+CiAgICAgICAgPG1pPng8L21pPgogICAgPC9tc3VwPgogICAgPG1pPik8L21pPgogICAgPG1pPj08L21pPgogICAgPG1pPjA8L21pPgo8L21hdGg+

2. Fie MathML (base64):PG1hdGg+CiAgICA8bXBoYW50b20+CiAgICAgICAgPG1nbHlwaCBzdHlsZT0iYm9yZGVyOjFweCIgd2lkdGg9IjAuNjZlbSIgaGVpZ2h0PSIxZW0iPjwvbWdseXBoPgogICAgPC9tcGhhbnRvbT4KICAgIDxtaT5mPC9taT4KICAgIDxtaT48L21pPgogICAgPG1vPiYjeDIyMDg7PC9tbz4KICAgIDxtaT48L21pPgogICAgPG1vPiYjeDIxMUQ7PC9tbz4KICAgIDxtbz5bPC9tbz4KICAgIDxtaT54PC9taT4KICAgIDxtbz5dPC9tbz4KICAgIDxtcGhhbnRvbT4KICAgICAgICA8bWdseXBoIHN0eWxlPSJib3JkZXI6MXB4IiB3aWR0aD0iMC42NmVtIiBoZWlnaHQ9IjFlbSI+PC9tZ2x5cGg+CiAgICA8L21waGFudG9tPgogICAgPG1pPiw8L21pPgogICAgPG1waGFudG9tPgogICAgICAgIDxtZ2x5cGggc3R5bGU9ImJvcmRlcjoxcHgiIHdpZHRoPSIwLjY2ZW0iIGhlaWdodD0iMWVtIj48L21nbHlwaD4KICAgIDwvbXBoYW50b20+CiAgICA8bWk+ZjwvbWk+CiAgICA8bWk+PTwvbWk+CiAgICA8bXN1cD4KICAgICAgICA8bWk+eDwvbWk+CiAgICAgICAgPG1pPjM8L21pPgogICAgPC9tc3VwPgogICAgPG1pPi08L21pPgogICAgPG1pPjQ8L21pPgogICAgPG1zdXA+CiAgICAgICAgPG1pPng8L21pPgogICAgICAgIDxtaT4yPC9taT4KICAgIDwvbXN1cD4KICAgIDxtaT4rPC9taT4KICAgIDxtaT5hPC9taT4KICAgIDxtaT54PC9taT4KICAgIDxtaT4rPC9taT4KICAgIDxtaT5iPC9taT4KPC9tYXRoPg==

a) Să se determine MathML (base64):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

b) Pentru MathML (base64):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, să se arate că MathML (base64):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

c) Pentru b=-4a, arătați că MathML (base64):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