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Question

Дано ответов: 2

25hjoerf10_zn · Answer 1 · 2018-05-27T10:50:44+0000

№13
3x² + 6.1x - 5.4 = 0
D = 6.1² + 4 * 3 * 5.4 = 37,21 + 64,8 = 102,01 = 10,1²

$x_{1} = \frac{-6.1 + 10.1}{2 * 3} = \frac{4}{6} = \frac{2}{3} \\ \\ x_{2} = \frac{-6.1-10.1}{2*3} = \frac{-16.2}{6} =- 2,7 \\$
Ответ: А.

№14
7x² - (1/5)x = 0
7x² - 0.2x = 0
х(7х - 0,2) = 0
x₁ = 0

7x₂ - 0.2 = 0
7x₂ = 0.2
x₂ = 0.2 : 7
x₂ = 1/35
Ответ: С.

№15
$\frac{4}{x-2} - \frac{4}{x} =1 \\ \\ 4x-4(x-2)=x(x-2) \\ 4x-4x+8= x^{2} -2x \\ x^{2} -2x-8=0 \\ D=-2 ^{2} +4*8=4+32=36= 6^{2} \\ \\ x_{1} = \frac{2+6}{2} =4 \\ \\ x_{2} = \frac{2-6}{2} =-2$
Ответ: D.

№16
(0,5 - 2x)(2x + 0.5) + (0.7 + x)² = 0.92 - 0.1x
0.25 - 4x² + 0,49 + 1,4х + х² = 0,92 - 0,1х
4х² - х² - 1,4х - 0,1х +0,92 - 0,25 - 0,49 = 0
3х² - 1,5х + 0,18 = 0
D = -1.5² - 4 * 3 * 0.18 = 2,25 - 2,16 = 0,09 = 0,3²

$x_{1} = \frac{1,5+0,3}{2*3} = \frac{1,8}{6} =0,3 \\ \\ x_{2} =\frac{1,5-0,3}{2*3} = \frac{1,2}{6} =0,2$
Ответ: А.

№17
20х² + х - 12 = 0
D = 1² + 4 * 20 * 12 = 1 + 960 = 961 = 31²
$x_{1} = \frac{-1+31}{2*20} = \frac{30}{40}= \frac{3}{4} \\ \\ x_{2} = \frac{-1-31}{2*20} =- \frac{32}{40} =- \frac{4}{5} \\$
Ответ: В.

№ 18
х² + 2,7х + 1,82 = 0
D = 2.7² - 4 * 1.82 = 7,29 - 7,28 = 0,01 = 0,1²
$x_{1} = \frac{-2,7+0,1}{2} = \frac{-2,6}{2} =-1,3 \\ \\ x_{2} = \frac{-2,7-0,1}{2} = \frac{-2,8}{2} =-1,4$
Ответ: D.

№ 19
42х² - 71х + 30 = 0
D = -71² - 4 * 42 * 30 = 5041 - 5040 = 1
$x_{1} = \frac{71+1}{2*42} = \frac{72}{84} = \frac{6}{7} \\ \\ x_{2} = \frac{71-1}{2*42} = \frac{70}{84} = \frac{35}{42} = \frac{5}{6} \\ \\ \frac{6}{7} = \frac{36}{42} \\ \\ \frac{5}{6} = \frac{35}{42} \\ \\ \frac{6}{7} \ \textgreater \ \frac{5}{6}$
Ответ:D.

oksik1970_zn · Answer 2 · 2018-05-27T10:50:44+0000

▪13.
ответ: А. х1= -2,7. х2= 2/3

$3 {x}^{2} + 6.1x - 5.4 = 0 \\ d = {b }^{2} - 4ac = 37.21 + 64.8 = 102.01 \\ x1 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 6.1 + \sqrt{102.01} }{6} = \frac{ - 6.1 + 10.1}{6} = \frac{4}{6} = \frac{2}{3} \\ x2 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 6.1 - \sqrt{102.01} }{6} = \frac{ - 6.1 - 10.1}{6} = \frac{ - 16.2}{6} = - \frac{162}{60} = \frac{ - 81}{30} = - \frac{27}{10} = - 2.7$
▪14.
Ответ: С. х1=0, х2 = 1/35

$7 {x}^{2} - \frac{1}{5} x = 0 \\ x(7x - \frac{1}{5} ) = 0 \\ x1 = 0 \\ - - - - - - \\ 7x - \frac{1}{5} = 0 \\ 7x = \frac{1}{5} \\ x = \frac{1}{5} \div 7 = \frac{1}{5 \times 7} = \frac{1}{35} \\ x2 = \frac{1}{35}$

▪15

Ответ: D. х1 = 4; х2 = -2

$\frac{4}{x - 2} - \frac{4}{x} = 1 \\ \frac{4x - 4(x - 2)}{x(x - 2)} = 1 \\ \frac{4x - 4x + 8}{ {x}^{2} - 2x} = 1 \\ {8} = {x}^{2} - 2x \\ {x}^{2} - 2x - 8 = 0 \\ d = 4 + 32 = 36 \\ x1 = \frac{ 2 + \sqrt{36} }{2} = \frac{8}{2} = 4 \\ x2 = \frac{2 - 6}{2} = - \frac{4}{2} = - 2$
▪16.

Ответ: А. х1 = 0,3. х2 = 0,2

$(0.5 - 2x)(2x + 0.5) + {(0.7 + x)}^{2} = 0.92 - 0.1x \\ 0.25 - 4 {x}^{2} + 0.49 + 1.4x + {x}^{2} + 0.1x - 0.92 = 0 \\ - 0.18 - 3 {x}^{2} + 1.5x = 0 \\ 3 {x}^{2} - 1.5x + 0.18 = 0 \\ d = 2.25 - 2.16 = 0.09 \\ x1 = \frac{ 1.5 + \sqrt{0.09} }{6} = \frac{1.5 + 0.3}{6} = \frac{1.8}{6} = 0.3 \\ x2 = \frac{ 1.5 - \sqrt{0.09} }{6} = \frac{1.5 - 0.3}{6} = \frac{1.2}{6} = 0.2$
▪17.

Ответ: В. х = -4/5
$20 {x}^{2} + x - 12 = 0 \\ d = 1 + 960 = 961 \\ x1 = \frac{ - 1 + \sqrt{961} }{40} = \frac{ - 1 + 31}{40} = \frac{30}{40} = \frac{3}{4} \\ x2 = \frac{ - 1 - 31}{40} = - \frac{32}{40} = - \frac{4}{5} = - 0.8$
▪18.

Ответ: D. х = -1,4

${x}^{2} + 2.7x + 1.82 = 0 \\ d = 7.29 - 7.28 = 0.01 \\ x1 = \frac{ - 2.7 + 0.1}{2} = \frac{ - 2.6}{2} = - 1.3 \\ x2 = \frac{ - 2.7 - 0.1}{2} = - \frac{2.8}{2} = - 1.4$
▪19.

Ответ: D. х = 6/7
$42 {x}^{2} - 71x + 30 = 0 \\ d = 5041 - 5040 = 1 \\ x1 = \frac{71 + 1}{84} = \frac{72}{84} = \frac{6}{7} \\ x2 = \frac{71 - 1}{84} = \frac{70}{84} = \frac{5}{6}$
сравним дроби приведя их к общему знаменателю
\frac{35}{42} \: \: \: \: znacit \\ \frac{6}{7} > \frac{5}{6} " alt=" \frac{6}{7} ... \frac{5}{6} \\ \frac{6 \times 6}{7 \times 6} ... \frac{5 \times 7}{6 \times 7} \\ \frac{36}{42} > \frac{35}{42} \: \: \: \: znacit \\ \frac{6}{7} > \frac{5}{6} " align="absmiddle" class="latex-formula">