1) Решите уравнение: 4х(х+3)=4-3х
2) Решите неравенство: 3х<5(x+1)-10<8
4) Запишите наименьшее из чисел: 6, 4√2, √33
5) Найдите значения выражения: при b = 3,75
frac{b+4}{b^{2}+16} * ( frac{b+4}{b-4} + frac{b-4}{b+4} )
Ответы
Ответ дал:
0
1.
4х(х + 3) = 4 - 3х
4х² + 12х = 4 - 3х
4х² + 12х - 4 + 3х = 0
4х² + 15х - 4 = 0
a=4 ; b = 15 ; с = - 4
D = b² - 4ac = 15² - 4*4*(-4) = 225 + 64 = 289 = 17²
D>0 - два корня уравнения
х₁ = ( - b - √D)/2a = (-15 - 17)/(2*4) = -32/8 = - 4
x₂ = (- b +√D)/2a = (-15+17)/(2*4) = 2/8 = 1/4 = 0.25
2.
3x < 5(x+1) - 10<8
3x < 5x + 5 - 10 <8
3x < 5x - 5 < 8
{ 5x - 5 > 3x
{ 5x - 5 < 8
{ 5x - 3x > 5
{ 5x < 8 + 5
{ 2x > 5
{ 5x < 13
{ x > 5/2
{ x < 13/5
{ x > 2.5
{ x < 2.6
2.5< x < 2.6
x∈ (2.5 ; 2,6)
4.
4√2 = √32
√33
6 = √36
4√2 < √33 < 6
ответ : 4√2
5.
![frac{b+4}{b^{2}+16} * ( frac{b+4}{b-4} + frac{b-4}{b+4} )= frac{b+4}{b^{2}+16} * frac{(b+4)(b+4)+(b - 4)(b - 4)}{(b-4)(b+4)} = \ \ =frac{b+4}{b^{2}+16} * frac{(b + 4)^2 + (b - 4)^2}{(b-4)(b+4)} = frac{b+4}{b^{2}+16} * frac{b^2+8b +16 + b^2 -8b+16}{(b - 4)(b+4)} = \ \ =frac{b+4}{b^{2}+16} * frac{2b^2+2*16}{(b-4)(b+4)} = frac{(b+4) * 2 *(b^2+16)}{(b^2+16)*(b-4)(b+4)} = frac{2}{b - 4} \ \ \ b= 3.75 \ frac{2}{3.75 - 4} = frac{2}{-0.25} = -8 frac{b+4}{b^{2}+16} * ( frac{b+4}{b-4} + frac{b-4}{b+4} )= frac{b+4}{b^{2}+16} * frac{(b+4)(b+4)+(b - 4)(b - 4)}{(b-4)(b+4)} = \ \ =frac{b+4}{b^{2}+16} * frac{(b + 4)^2 + (b - 4)^2}{(b-4)(b+4)} = frac{b+4}{b^{2}+16} * frac{b^2+8b +16 + b^2 -8b+16}{(b - 4)(b+4)} = \ \ =frac{b+4}{b^{2}+16} * frac{2b^2+2*16}{(b-4)(b+4)} = frac{(b+4) * 2 *(b^2+16)}{(b^2+16)*(b-4)(b+4)} = frac{2}{b - 4} \ \ \ b= 3.75 \ frac{2}{3.75 - 4} = frac{2}{-0.25} = -8](https://tex.z-dn.net/?f=frac%7Bb%2B4%7D%7Bb%5E%7B2%7D%2B16%7D+%2A+%28+frac%7Bb%2B4%7D%7Bb-4%7D+%2B+frac%7Bb-4%7D%7Bb%2B4%7D+%29%3D+frac%7Bb%2B4%7D%7Bb%5E%7B2%7D%2B16%7D+%2A+frac%7B%28b%2B4%29%28b%2B4%29%2B%28b+-+4%29%28b+-+4%29%7D%7B%28b-4%29%28b%2B4%29%7D+%3D+%5C+%5C+%3Dfrac%7Bb%2B4%7D%7Bb%5E%7B2%7D%2B16%7D+%2A+frac%7B%28b+%2B+4%29%5E2+%2B+%28b+-+4%29%5E2%7D%7B%28b-4%29%28b%2B4%29%7D+%3D+frac%7Bb%2B4%7D%7Bb%5E%7B2%7D%2B16%7D+%2A+frac%7Bb%5E2%2B8b+%2B16+%2B+b%5E2+-8b%2B16%7D%7B%28b+-+4%29%28b%2B4%29%7D+%3D+%5C+%5C+%3Dfrac%7Bb%2B4%7D%7Bb%5E%7B2%7D%2B16%7D+%2A+frac%7B2b%5E2%2B2%2A16%7D%7B%28b-4%29%28b%2B4%29%7D+%3D+frac%7B%28b%2B4%29+%2A+2+%2A%28b%5E2%2B16%29%7D%7B%28b%5E2%2B16%29%2A%28b-4%29%28b%2B4%29%7D+%3D+frac%7B2%7D%7Bb+-+4%7D+%5C+%5C+%5C+b%3D+3.75+%5C+frac%7B2%7D%7B3.75+-+4%7D+%3D+frac%7B2%7D%7B-0.25%7D+%3D+-8)
4х(х + 3) = 4 - 3х
4х² + 12х = 4 - 3х
4х² + 12х - 4 + 3х = 0
4х² + 15х - 4 = 0
a=4 ; b = 15 ; с = - 4
D = b² - 4ac = 15² - 4*4*(-4) = 225 + 64 = 289 = 17²
D>0 - два корня уравнения
х₁ = ( - b - √D)/2a = (-15 - 17)/(2*4) = -32/8 = - 4
x₂ = (- b +√D)/2a = (-15+17)/(2*4) = 2/8 = 1/4 = 0.25
2.
3x < 5(x+1) - 10<8
3x < 5x + 5 - 10 <8
3x < 5x - 5 < 8
{ 5x - 5 > 3x
{ 5x - 5 < 8
{ 5x - 3x > 5
{ 5x < 8 + 5
{ 2x > 5
{ 5x < 13
{ x > 5/2
{ x < 13/5
{ x > 2.5
{ x < 2.6
2.5< x < 2.6
x∈ (2.5 ; 2,6)
4.
4√2 = √32
√33
6 = √36
4√2 < √33 < 6
ответ : 4√2
5.
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