Question

25а2+ 10а+ 1 : 5а2- 9а- 2

Answer 1

$frac{25a^2+10a+1}{5a^2-9a-2}=?\\25a^2+10a+1=(5a)^2+2*5a*1+1^2=(5a+1)^2\\5a^2-9a-2=5(a-2)(a+0,2)\D=(-9)^2-4*5*(-2)=81+40=121=11^2\a_1= frac{9+11}{2*5}= frac{20}{10}=2\a_2= frac{9-11}{2*5}= frac{-2}{10}=-0,2\\ frac{25a^2+10a+1}{5a^2-9a-2}= frac{(5a+1)^2}{5(a-2)(a+0,2)}= frac{25(a+0,2)^2}{5(a-2)(a+0,2)}= frac{5(a+0,2)}{a-2}$