![[tex]7x^2+20x-14=5\sqrt{x^4-20x^2+4}\\\sqrt{x^4-20x^2+4}\geq0\\x^4-20x^2+4\geq0\\(x^2+4x-2)(x^2-4x-2)\geq0\\x^2+4x-2=0\\x_1=-2+\sqrt{6}; x_2=-2-\sqrt{6}\\x^2-4x^2-2=0\\x_1=2+\sqrt{6}; x_2=2-\sqrt{6}\\](https://tex.z-dn.net/?f=%5Btex%5D7x%5E2%2B20x-14%3D5%5Csqrt%7Bx%5E4-20x%5E2%2B4%7D%5C%5C%5Csqrt%7Bx%5E4-20x%5E2%2B4%7D%5Cgeq0%5C%5Cx%5E4-20x%5E2%2B4%5Cgeq0%5C%5C%28x%5E2%2B4x-2%29%28x%5E2-4x-2%29%5Cgeq0%5C%5Cx%5E2%2B4x-2%3D0%5C%5Cx_1%3D-2%2B%5Csqrt%7B6%7D%3B%20x_2%3D-2-%5Csqrt%7B6%7D%5C%5Cx%5E2-4x%5E2-2%3D0%5C%5Cx_1%3D2%2B%5Csqrt%7B6%7D%3B%20x_2%3D2-%5Csqrt%7B6%7D%5C%5C "[tex]7x^2+20x-14=5\sqrt{x^4-20x^2+4}\\\sqrt{x^4-20x^2+4}\geq0\\x^4-20x^2+4\geq0\\(x^2+4x-2)(x^2-4x-2)\geq0\\x^2+4x-2=0\\x_1=-2+\sqrt{6}; x_2=-2-\sqrt{6}\\x^2-4x^2-2=0\\x_1=2+\sqrt{6}; x_2=2-\sqrt{6}\\")
\\ 5\sqrt{x^4-20x^2+4}=7x^2+20x-14\\25(x^4-20x^2+4)=49x^4+400x^2+196+280x^3-196^2-520x\\25(x^4-20x^2+4)-49x^4-400x^2-196-280x^3+196^2+520x=0\\25x^4-500x^2+100-49x^4-400x^2-196-280x^3+196^2+520x=0\\-24x^4-704x^2-96-280x^3+560=0\\-8(3x^4-6x^2+100x^2-6x^2+12+16x^3+20x^3-40x-30x)=0\\3x^4-6x^2+100x^2-6x^2+12+16x^3+20x^3-40x-30x=0\\3x^2(x^2+5x-2)+20x(x^2+5x-2)[\tex]
х∈[-∞;-2-√6]∪[-2-√6;-2+√6]∪[2+√6;+∞]
Теперь находим корни уровнения.
