9xˇ2-xˇ6=xˇ2(9-xˇ4)=xˇ2 (3+xˇ2)(3-xˇ2)=...........xˇ2(3+xˇ2)(V(3)+x)(V(3)-x)
√63 - 3√1,75 - 0,5√343 + √112 = √(9*7) - 3*√7*(1/4) - 0,5*√(49*7) + √(16*7) =
= 3√7 - 1,5√7 - 3,5√7 + 4√7 = 2√7
Ответ:
4
Объяснение:
Найти f(√2) , если f ( x-1/х)= x²+1/х²
замена:
![\displaystyle\\t=x-\frac{1}{x}\\\\t^2=(x-\frac{1}{x})^2=x^2-2x*\frac{1}{x}+\frac{1}{x^2} =x^2+\frac{1}{x^2}-2\\\\x^2+\frac{1}{x^2} =t^2+2\\\\f(t)=t^2+2\\\\f(\sqrt{2})=(\sqrt{2})^2+2=2+2=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5Ct%3Dx-%5Cfrac%7B1%7D%7Bx%7D%5C%5C%5C%5Ct%5E2%3D%28x-%5Cfrac%7B1%7D%7Bx%7D%29%5E2%3Dx%5E2-2x%2A%5Cfrac%7B1%7D%7Bx%7D%2B%5Cfrac%7B1%7D%7Bx%5E2%7D%20%3Dx%5E2%2B%5Cfrac%7B1%7D%7Bx%5E2%7D-2%5C%5C%5C%5Cx%5E2%2B%5Cfrac%7B1%7D%7Bx%5E2%7D%20%3Dt%5E2%2B2%5C%5C%5C%5Cf%28t%29%3Dt%5E2%2B2%5C%5C%5C%5Cf%28%5Csqrt%7B2%7D%29%3D%28%5Csqrt%7B2%7D%29%5E2%2B2%3D2%2B2%3D4)