Question

(а2+100b2-20ab):(b2), если а/b = 2010

Answer 1

$frac{a^2 + 100b^2 - 20ab}{b^2} = frac{(a-10b)^2}{b^2} = frac{(a-10b)(a-10b)}{b*b} = frac{a-10b}{b} * frac{a-10b}{b} =$$( frac{a}{b} - frac{10b}{b})( frac{a}{b} - frac{10b}{b}) = (frac{a}{b} - 10)( frac{a}{b} - 10) = (2010 - 10)(2010-10) =$$2000*2000 = 4000000$