Question

Кто может помочь? За решение любых заданий дам баллов! Помогите

Answer 1

Задание 1.
============== 1 ==============
$frac{y^2-11y-26}{9y+18}\ y^2-11y-26=0\ D=b^2-4ac=(-11)^2-4cdot1cdot(-26) =121+104=225=15^2\ y_1= frac{11+15}{2}= 13\ y_2= frac{11-15}{2}= -2\ y^2-11y-26=(y-13)(y+2)\ frac{y^2-11y-26}{9y+18}= frac{(y-13)(y+2)}{9(y+2)}= frac{y-13}{9} \ y=-5 rightarrow frac{-5-13}{9}= frac{-18}{9}=-2\ y=31 rightarrow frac{31-13}{9}= frac{18}{9}=2\ y=112 rightarrow frac{112-13}{9}= frac{99}{9}=11$
============== 2 ==============
$frac{x^2-18x+80}{5x-50} \ x^2-18x+80=0\ D=b^2-4ac=(-18)^2-4cdot1cdot80=324-320=4=2^2\ x_1= frac{18+2}{2} =10\ x_2= frac{18-2}{2} =8\ x^2-18x+80=(x-10)(x-8)\ frac{x^2-18x+80}{5x-50}= frac{(x-10)(x-8)}{5(x-10)}= frac{x-8}{5} \ x=-12 rightarrow frac{-12-8}{5}= frac{-20}{5}= -4\ x=8.5 rightarrow frac{8.5-8}{5}= frac{0.5}{5}= 0.1\ x=48 rightarrow frac{48-8}{5}= frac{40}{5}= 8$
============== 3 ==============
$frac{x^2-8x-33}{10x+30} \ x^2-8x-33 = 0\ D=b^2-4ac=(-8)^2-4cdot1cdot(-33)=64+132=196=14^2\ x_1= frac{8+14}{2} =11\ x_2= frac{8-14}{2} =-3\ x^2-8x-33 =(x-11)(x+3)\ frac{x^2-8x-33}{10x+30} = frac{(x-11)(x+3)}{10(x+3)} = frac{x-11}{10}\ x=-9 rightarrow frac{-9-11}{10}= frac{-20}{5}= -4\ x=12 rightarrow frac{12-11}{10}= frac{1}{10}\ x=111 rightarrow frac{111-11}{10}= frac{100}{5}= 20$
============== 4 ==============
$frac{8y-56}{y^2-27y+140}\ y^2-27y+140=0\ D=b^2-4ac=(-27)^2-4cdot1cdot140=729-560=169=13^2\ y_1= frac{27+13}{2}= frac{40}{2}=20\ y_2= frac{27-13}{2}= frac{14}{2}=7\ y^2-27y+140= (y-20)(y-7)\ frac{8y-56}{y^2-27y+140}= frac{8(y-7)}{(y-20)(y-7)}= frac{8}{y-20}\ y = -4 rightarrow frac{8}{-4-20}= frac{8}{-24}= - frac{1}{3}\ y = 22.5 rightarrow frac{8}{22.5-20}= frac{8}{2.5}= 3.2\ y = 24 rightarrow frac{8}{24-20}= frac{8}{4}= 2$

Задание 2.
============== 1 ==============
$frac{2.5+3.48}{6.34}= frac{5.98}{6.34} =5 frac{98}{100}:6 frac{34}{100}= 5 frac{49}{50}:6 frac{17}{50}= frac{299}{50} cdot frac{50}{317}= frac{299}{317}$
============== 2 ==============
$frac{2.5cdot3.48}{6.34}= frac{8.7}{6.34} =8 frac{7}{10}:6 frac{34}{100}= frac{87}{10} cdot frac{50}{317}= frac{87 cdot5}{317}= frac{435}{317} =1 frac{118}{317}$
============== 3 ==============
$frac{2.5}{6.34+3.48}= frac{2.5}{9.82} =2 frac{5}{10}:9 frac{82}{100}= 2 frac{1}{2}:9 frac{41}{50}= frac{5}{2} cdot frac{50}{491} = frac{5cdot25}{491}= frac{125}{491}$
============== 4 ==============
$frac{2.5}{6.34cdot3.48}= frac{2 frac{5}{10} }{6 frac{34}{100}cdot 3 frac{48}{100} } =frac{2 frac{1}{2} }{6 frac{17}{50}cdot 3 frac{12}{25} } =frac{ frac{5}{2} }{ frac{317}{50}cdot frac{87}{25} } = frac{5}{2}cdot frac{50 cdot 25}{317cdot87} = frac{3125}{27579}$
============== 5 ==============
$2.7(18^2-5^2)=2.7(18-5)(18+5)=2.7 cdot 13 cdot 23 = 807.3$
============== 6 ==============
$(1+ sqrt{ frac{a-x}{a+x} } )(1- sqrt{ frac{a-x}{a+x} } )=1^2- (sqrt{ frac{a-x}{a+x} })^2=1- frac{a-x}{a+x} }= frac{a+x-a+x}{a+x} =\ = frac{2x}{a+x} \ a=5, x=4 rightarrow frac{2x}{a+x} = frac{2cdot4}{5+4}= frac{8}{9}$