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Ответ

Ответ дан
Бориссс

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

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