Question

Помогите решить уравнения с помощью дисриминанта:

1.(х+4)(в квадрате)=4х(в квадрате) +5

2.9х(4х-1)=3х-1

3.0,09-4х(в квадрате)=1,6х

4.0,1х(в квадрате) -14= -0,4х

5.(х-4)(4х-3)+3=0

6.(х+5)(в квадрате) + (х-2)(в квадрате) + (х-7)(х+7)=11х +80

Answer 1

 

 

 

1)$(x 4)^{2}=4x^{2} 5</var>$</p> <p><var> </var> <img src=[/tex]x^{2}+8x+16=4x^{2}+5 " title=" x^{2}+8x+16=4x^{2}+5 " alt=" x^{2}+8x+16=4x^{2}+5 " />

$<var>-3x^{2}+8x+11=0</var>$

D=64+132=196

$<var>x_{1}=frac{8+sqrt{196}}{6}=frac{22}{6}=3frac{4}{6}=3frac{2}{3}</var>$

$<var>x_{2}=frac{8-sqrt{196}}{6}=frac{-6}{6}=-1$

$<var>x^{2}+8x+16=4x^{2}+5</var>$

$<var>-3x^{2}+8x+11=0</var>$

D=64+132=196

$<var>x_{1}=frac{8+sqrt{196}}{6}=frac{22}{6}=3frac{4}{6}=3frac{2}{3}</var>$

$(x+4)^{2}=4x^{2}+5</var>$

$<var>x^{2}+8x+16=4x^{2}+5</var>$

$<var>-3x^{2}+8x+11=0</var>$

D=64+132=196

$<var>x_{1}=frac{8+sqrt{196}}{6}=frac{22}{6}=3frac{4}{6}=3frac{2}{3}</var>$

$<var>x_{2}=frac{8-sqrt{196}}{6}=frac{-6}{6}=-1$

2)$9x(4x-1)=3x-1</var>$

2)$<var>x_{2}=frac{8-sqrt{196}}{6}=frac{-6}{6}=-1$

2)$9x(4x-1)=3x-1</var>$

$<var> 36x^{2}-9x-3x+1=0</var>$

$<var>36x^{2}-12x+1=0</var>$

D=144-144=0

$<var>x_{1}=frac{12}{2*36}=frac{12}{72}=frac{1}{6}$

$<var> 36x^{2}-9x-3x+1=0</var>$

$<var>36x^{2}-12x+1=0</var>$

D=144-144=0

$9x(4x-1)=3x-1</var>$

$<var> 36x^{2}-9x-3x+1=0</var>$

$<var>36x^{2}-12x+1=0</var>$

D=144-144=0

$<var>x_{1}=frac{12}{2*36}=frac{12}{72}=frac{1}{6}$

3)$0,09-4x^{2}=1,6x</var>$

3)$<var>x_{1}=frac{12}{2*36}=frac{12}{72}=frac{1}{6}$

3)$0,09-4x^{2}=1,6x</var>$

$<var>-4x^{2}-1,6x+0,09=0</var>$

D=2,56+1,44=4

$<var>x_{1}=frac{1,6+sqrt{4}}{-8}=frac{3,6}{-8}=-0,45</var>$

$<var>x_{2}=frac{1,6-sqrt{4}}{-8}=frac{-0,4}{-8}=0,05$

$<var>-4x^{2}-1,6x+0,09=0</var>$

D=2,56+1,44=4

$<var>x_{1}=frac{1,6+sqrt{4}}{-8}=frac{3,6}{-8}=-0,45</var>$

$0,09-4x^{2}=1,6x</var>$

$<var>-4x^{2}-1,6x+0,09=0</var>$

D=2,56+1,44=4

$<var>x_{1}=frac{1,6+sqrt{4}}{-8}=frac{3,6}{-8}=-0,45</var>$

$<var>x_{2}=frac{1,6-sqrt{4}}{-8}=frac{-0,4}{-8}=0,05$

 

 

4) $0<var>,1x^{2}-14=-0,4x</var> " title=" <var>x_{2}=frac{1,6-sqrt{4}}{-8}=frac{-0,4}{-8}=0,05" /></var></p> <p> </p> <p> </p> <p>4) [tex]0<var>,1x^{2}-14=-0,4x</var> " alt=" <var>x_{2}=frac{1,6-sqrt{4}}{-8}=frac{-0,4}{-8}=0,05" /></var></p> <p> </p> <p> </p> <p>4) [tex]0<var>,1x^{2}-14=-0,4x</var> " /> <var> </var></p> <p>[tex] <var>0,1x^{2}+0,4x-14=0</var>$

D=0,16+5,6=5,76

$<var>x_{1}=frac{-0,4-sqrt{5,76}}{0,2}=frac{-0,4-2,4}{0,2}=frac{-2,8}{0,2}=-1,4</var>$ $<var>x_{2}=frac{-0,4+sqrt{5,76}}{0,2}=frac{-0,4+2,4}{0,2}=frac{2}{0,2}=10</var>$

 

5) $(x-4)(4x-3) 3=0 </var>$</p> <p><img src=[/tex]4x^{2}-16x-3x+12+3=0 " title=" 4x^{2}-16x-3x+12+3=0 " alt=" 4x^{2}-16x-3x+12+3=0 " />

$<var>4x^{2}-19x+15=0</var>$

D=361-240=121

$<var>x_{1}=frac{19+sqrt{121}}{8}=frac{30}{8}=frac{15}{4}=3frac{3}{4} </var>$

$<var>x_{2}=frac{19-sqrt{121}}{8}=frac{8}{8}=1$

$<var>4x^{2}-16x-3x+12+3=0 </var>$

$<var>4x^{2}-19x+15=0</var>$

D=361-240=121

$<var>x_{1}=frac{19+sqrt{121}}{8}=frac{30}{8}=frac{15}{4}=3frac{3}{4} </var>$

$(x-4)(4x-3)+3=0 </var>$

$<var>4x^{2}-16x-3x+12+3=0 </var>$

$<var>4x^{2}-19x+15=0</var>$

D=361-240=121

$<var>x_{1}=frac{19+sqrt{121}}{8}=frac{30}{8}=frac{15}{4}=3frac{3}{4} </var>$

$<var>x_{2}=frac{19-sqrt{121}}{8}=frac{8}{8}=1$

6)$(x 5)^{2} (x-2)^{2} (x-7)(x 7)=11x 80</var>$

6)$<var>x_{2}=frac{19-sqrt{121}}{8}=frac{8}{8}=1$

6)$(x 5)^{2} (x-2)^{2} (x-7)(x 7)=11x 80</var>$

$<var> x^{2}+10x+25+x^{2}-4x+4+x^{2}-49+11x-80=0</var>$

$<var>3x^{2}-5x-100=0</var>$

D=25+1200=1225

$<var>x_{1}=frac{5+sqrt{1225}}{6}=frac{40}{6}=frac{20}{3}=6frac{2}{3}</var>$

$<var>x_{2}=frac{5-sqrt{1225}}{6}=frac{-30}{6}=-6$

$<var> x^{2}+10x+25+x^{2}-4x+4+x^{2}-49+11x-80=0</var>$

$<var>3x^{2}-5x-100=0</var>$

D=25+1200=1225

$<var>x_{1}=frac{5+sqrt{1225}}{6}=frac{40}{6}=frac{20}{3}=6frac{2}{3}</var>$

$(x+5)^{2}+(x-2)^{2}+(x-7)(x+7)=11x+80</var>$

$<var> x^{2}+10x+25+x^{2}-4x+4+x^{2}-49+11x-80=0</var>$

$<var>3x^{2}-5x-100=0</var>$

D=25+1200=1225

$<var>x_{1}=frac{5+sqrt{1225}}{6}=frac{40}{6}=frac{20}{3}=6frac{2}{3}</var>$

[tex] x_{2}=frac{5-sqrt{1225}}{6}=frac{-30}{6}=-6" />