√5+ √3 / √5 - √3 + √5 - √3/√5+ √3 - √5+1/√5+-1

1.

а) (3y - 2)(3y + 2) = 9y² - 4

б) (3y - 1)² = 9y² - 6y + 1

в) (4a + 3k)(4a - 3k) = 16a² - 9k²

2.

(b-8)² - (64 - 6b) = b² - 16b + 64 - 64 + 6b = b² - 10b = b(b - 10)

3.

a) 25 - y² = (5 - y)(5 + y)

б) a² - 6ab + 9b² = a² - 2×1×3ab + (3b)² = (a - 3b)²

4.

36 - (6 - x)² = x(2,5 - x)

36 - (36 - 12x + x²) = 2,5x - x²

12x + x² = 2,5x - x²

2x² + 9,5x = 0

x(2x + 9,5) = 0

x = 0 или 2x = -9,5

x = 0 или x = -4,75

ответ: 0; -4,75

5.

а) (c² - 3a)(3a - c²) = -(3a - c²)(3a - c²) = -(3a-c²)²

б) (3x + x³)² = 9x² + 6x⁴ + x⁶

в) (3 - k)²(k+3)² = (3 - k)²(3+k)² = [(3-k)(3+k)]² = (9 - k²)²

6.

а) (3x - 2)² - (3x - 4)(4 + 3x) = 0

(3x - 2)² + (4 + 3x)² = 0

9x² - 12x + 4 + 16 + 24x + 9x² = 0

12x + 20 = 0

12x = -20

3x = -5

x = -5/3

б) 25y² - 64 = 0

y² = 64/25

y = ± 8/5

7.

а) 36a⁴ - 25a²b² = a²(36a² - 25b²) = a²(6a - 5b)(6a + 5b)

б) (x - 7)² - 81 = (x - 7 - 9)(x - 7 + 9) = (x - 16)(x + 2)

А
1)3^4=81
2)1/3*81=27
3)2*0,12=0,24
4)27-0,24=26,76
5)(0,1)²=0,01
6)0,13+0,01=0,14
7)26,76:0,14=2676:14=191 1/7
8)191 1/7:3=1338/7*1/3=1338/21=63 15/21=63 5/7
б
1)(7/5)³=343/125
2)25²=625
3)343/125*625=343*5=1715
4)11:2=5,5
5)1715-5,5=1709,5
6)1709,5*1000=1709500
в
1)2^10:2^4=2^6=64
2)3^5:3^2=3³=27
3)64+27=91
4)91-11=80
5)(0,2)³=0,008
6)80*0,008=0,64
г
1)5/6+7/8=(20+21)/24=41/24
2)5/6-7/8=(20-21)/24=-1/24
3)3^4=81
4)41/24*81=41*27/8=1107/8
5)4³=64
6)-1/24*64=-8/3
7)1107/8+8/3=(3321+64)/24=3385/24
8)(-3/5)³=-27/125
9)3385/24:(-27/125)=-(3385*125)/(24*27)=-423125/648=-652 629/648