Question

32.29. 1) (4x-3)(4х + 3) - (4x-1)^2 <3x; 2) 3(x-1)- 3x(х - 5) > 21;3) 10(х-2)^2 – 5x(2x-1) <-30;4) (5х + 6)^2 - (5x - 6)2^2> 12.32.30. 1) (3x-1)2 - 7 < (9x + 2)x + 2;2) 2x(8х + 3) +1> (5 - 4x)^2 - 1;3) (0,3х +0,2)^2 +0,58x > 3,9 - (2 - 0,3х)(2 +0,3х);4) (0,2-0,8х)^2 + 11,16 < (0,5 + 0,8х)^2 — 0,25.​

Answer 1

Ответ:

1) (4х-3)(4х+3)-(4х-1)^2=3х

16х^2-9-(16х^2-8х+1)=3х

16х^2-9-16х^2+8х-1=3х

5х=10

х=2

2) 3(х-1)^2-3х(х-5)=21

3(х^2-2х+1)-3х^2+15х=21

3х^2-6х+3-3х^2+15х=21

9х=18

х=2

3) 10(х-2)^2-5х(2х-1)=-4

10х^2-40х+40-10х^2+5х=-4

-35х=-44

х=44/35

4) (5х+6)^2-(5х-6)^2=13

25х^2+60х+36-25х^2+60х-36=13

120х=13

х=13/120

вроде так

Answer 2

Sure! Let's solve each inequality one by one.

1. (4x-3)(4x + 3) - (4x-1)^2 < 3x

Expanding the expressions: (16x^2 - 9) - (16x^2 - 8x + 1) < 3x

Simplifying further: 16x^2 - 9 - 16x^2 + 8x - 1 < 3x 8x - 10 < 3x

Moving variables to one side: 8x - 3x < 10 5x < 10

Dividing both sides by 5: x < 2

2. 3(x-1) - 3x(x - 5) > 21

Expanding and simplifying: 3x - 3 - 3x^2 + 15x > 21 -3x^2 + 18x - 3 > 21

Rearranging the terms: -3x^2 + 18x - 24 > 0

Dividing by -3 to simplify the inequality (note that dividing by a negative number reverses the inequality): x^2 - 6x + 8 < 0

Factoring the quadratic: (x - 4)(x - 2) < 0

The solutions for this inequality are the values of x for which the expression is negative. We can use a sign chart or test intervals to find the solution. The solution is: 2 < x < 4

3. 10(x-2)^2 - 5x(2x-1) < -30

Expanding and simplifying: 10x^2 - 40x + 40 - 10x^2 + 5x < -30 -35x + 40 < -30

Simplifying further: -35x < -70 x > 2

4. (5x + 6)^2 - (5x - 6)^2 > 12.32

Expanding the expressions: 25x^2 + 60x + 36 - 25x^2 + 60x - 36 > 12.32

Simplifying: 120x > 12.32 x > 0.1033

Please note that for inequalities involving decimal numbers, I have rounded the solutions to a reasonable number of decimal places.