1) , x ∈ [1/27; 1]
Ответ: Область значений [1; 9]
3) а)
б)
4) а)
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Answers & Comments
1)
, x ∈ [1/27; 1]
Ответ: Область значений [1; 9]
3) а)![\sqrt[3]{343}-2\sqrt[4]{16} +\sqrt[5]{243} + \sqrt{256}=7-2*2+3+16= 22 \sqrt[3]{343}-2\sqrt[4]{16} +\sqrt[5]{243} + \sqrt{256}=7-2*2+3+16= 22](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B343%7D-2%5Csqrt%5B4%5D%7B16%7D%20%2B%5Csqrt%5B5%5D%7B243%7D%20%2B%20%5Csqrt%7B256%7D%3D7-2%2A2%2B3%2B16%3D%2022)
б)![\sqrt[3]{-27*2^6*2^{12}}=-\sqrt[3]{3^3*2^18} =-3*2^6=-3*64 = -192 \sqrt[3]{-27*2^6*2^{12}}=-\sqrt[3]{3^3*2^18} =-3*2^6=-3*64 = -192](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B-27%2A2%5E6%2A2%5E%7B12%7D%7D%3D-%5Csqrt%5B3%5D%7B3%5E3%2A2%5E18%7D%20%3D-3%2A2%5E6%3D-3%2A64%20%3D%20-192)
4) а)![\frac{\sqrt{a} }{a^{1/2} + b^{1/2}} + \frac{\sqrt{b} }{a^{1/2} - b^{1/2}}=\frac{\sqrt{a}(\sqrt{a} -\sqrt{b} ) +\sqrt{b}(\sqrt{a} +\sqrt{b}) }{(\sqrt{a} -\sqrt{b})(\sqrt{a} +\sqrt{b})} =\frac{a-\sqrt{ab} +\sqrt{ab} +b}{a-b} =\frac{a+b}{a-b} \frac{\sqrt{a} }{a^{1/2} + b^{1/2}} + \frac{\sqrt{b} }{a^{1/2} - b^{1/2}}=\frac{\sqrt{a}(\sqrt{a} -\sqrt{b} ) +\sqrt{b}(\sqrt{a} +\sqrt{b}) }{(\sqrt{a} -\sqrt{b})(\sqrt{a} +\sqrt{b})} =\frac{a-\sqrt{ab} +\sqrt{ab} +b}{a-b} =\frac{a+b}{a-b}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Ba%7D%20%7D%7Ba%5E%7B1%2F2%7D%20%2B%20b%5E%7B1%2F2%7D%7D%20%2B%20%5Cfrac%7B%5Csqrt%7Bb%7D%20%7D%7Ba%5E%7B1%2F2%7D%20-%20b%5E%7B1%2F2%7D%7D%3D%5Cfrac%7B%5Csqrt%7Ba%7D%28%5Csqrt%7Ba%7D%20-%5Csqrt%7Bb%7D%20%29%20%2B%5Csqrt%7Bb%7D%28%5Csqrt%7Ba%7D%20%2B%5Csqrt%7Bb%7D%29%20%7D%7B%28%5Csqrt%7Ba%7D%20-%5Csqrt%7Bb%7D%29%28%5Csqrt%7Ba%7D%20%2B%5Csqrt%7Bb%7D%29%7D%20%3D%5Cfrac%7Ba-%5Csqrt%7Bab%7D%20%2B%5Csqrt%7Bab%7D%20%2Bb%7D%7Ba-b%7D%20%3D%5Cfrac%7Ba%2Bb%7D%7Ba-b%7D)
б)![\frac{\sqrt{xy}*\sqrt[4]{x} }{(x+y)*\sqrt[4]{\frac{y^2}{x} } } -\frac{x^2+y^2}{x^2-y^2} =\frac{\sqrt{x} *\sqrt{y}*\sqrt[4]{x}*\sqrt[4]{x} }{(x+y)*\sqrt[4]{y^2} } -\frac{x^2+y^2}{x^2-y^2}=\frac{\sqrt{x} *\sqrt{x} }{x+y} -\frac{x^2+y^2}{x^2-y^2}= \frac{\sqrt{xy}*\sqrt[4]{x} }{(x+y)*\sqrt[4]{\frac{y^2}{x} } } -\frac{x^2+y^2}{x^2-y^2} =\frac{\sqrt{x} *\sqrt{y}*\sqrt[4]{x}*\sqrt[4]{x} }{(x+y)*\sqrt[4]{y^2} } -\frac{x^2+y^2}{x^2-y^2}=\frac{\sqrt{x} *\sqrt{x} }{x+y} -\frac{x^2+y^2}{x^2-y^2}=](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Bxy%7D%2A%5Csqrt%5B4%5D%7Bx%7D%20%7D%7B%28x%2By%29%2A%5Csqrt%5B4%5D%7B%5Cfrac%7By%5E2%7D%7Bx%7D%20%7D%20%7D%20-%5Cfrac%7Bx%5E2%2By%5E2%7D%7Bx%5E2-y%5E2%7D%20%3D%5Cfrac%7B%5Csqrt%7Bx%7D%20%2A%5Csqrt%7By%7D%2A%5Csqrt%5B4%5D%7Bx%7D%2A%5Csqrt%5B4%5D%7Bx%7D%20%7D%7B%28x%2By%29%2A%5Csqrt%5B4%5D%7By%5E2%7D%20%7D%20%20-%5Cfrac%7Bx%5E2%2By%5E2%7D%7Bx%5E2-y%5E2%7D%3D%5Cfrac%7B%5Csqrt%7Bx%7D%20%2A%5Csqrt%7Bx%7D%20%7D%7Bx%2By%7D%20-%5Cfrac%7Bx%5E2%2By%5E2%7D%7Bx%5E2-y%5E2%7D%3D)