Question

Найти значение (b-1/b)^2 если (b+1/b)^2=8

Answer 1

$left(b+ frac{1}{b}right)^2=8$

$b^2+2 cdot b cdot frac{1}{b} + frac{1}{b^2}=8$

$b^2+2 + frac{1}{b^2}=8$

$b^2+frac{1}{b^2}=8-2$

$b^2+ frac{1}{b^2}=6$

$left(b- frac{1}{b}right)^2=b^2-2 cdot b cdot frac{1}{b} + frac{1}{b^2}=$

$b^2-2+ frac{1}{b^2}=6-2=4$