Question

докажите, что 1) 4х+3у>14​

Answer 1

Объяснение:

$x > \frac{1}{2}\\\\4\cdot x > 4\cdot\frac{1}{2}\\\\4x > 2$

$y > 4\\\\3\cdot y > 3\cdot4\\\\3y > 12$

$(\ 4x > 2 \ \land \ 3y > 12 \ ) \Rightarrow 4x+3y > 2+12=14$

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$(\ x > \frac{1}{2} \ \land \ y > 4 \ ) \Rightarrow xy > \frac{1}{2}\cdot4\\\\xy > \frac{4}{2}\\\\xy > 2\\\\xy\cdot2 > 2\cdot2\\\\2xy > 4\\\\2xy-3 > 4-3\\\\2xy-3 > 1$

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$x > \frac{1}{2}\\\\x^{2} > (\frac{1}{2})^{2}\\\\x^{2} > \frac{1}{4}\\\\( \ x^{2} > \frac{1}{4} \ \land \ y > 4 \ ) \Rightarrow x^{2}y > \frac{1}{4}\cdot4=1$

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$x > \frac{1}{2}\\\\x^{3} > (\frac{1}{2})^{3}\\\\x^{3} > \frac{1}{8}$

$y > 4\\\\y^{2} > 4^{2}\\\\y^{2} > 16$

$(\ x^{3} > \frac{1}{8} \ \land \ y^{2} > 16 \ ) \Rightarrow x^{3}+y^{2} > \frac{1}{8}+16 > 16$