1)а) (1/5+8/15)×6 = (3/15 + 8/15) × 6 = (11/15) × 6 = 66/15 = 4.4б) -13×(-9.3-7.8) = -13×(-17.1) = 219.3в) 4√5×3√3×√15 = 4√(5×3×15) = 4√(225) = 4×15 = 60
2)а) - 1/5x^2+20 = 0
б) 1/3x^2-27 = 01/3x^2 = 27x^2 = 81x = ±9
в) 1/4x^2-4 = 01/4x^2 = 4x^2 = 16x = ±4
г) x^2+6=5xx^2 - 5x + 6 = 0(x - 2)(x - 3) = 0x = 2 or x = 3
д) x^2-21=4xx^2 - 4x - 21 = 0(x - 7)(x + 3) = 0x = 7 or x = -3
е) x+x/5=-12/55x + x = -126x = -12x = -2
ж) x+x/11=24/1111x + x = 2412x = 24x = 2
3) Подставляем a = 9√8 + 4 и b = √8 - 4 в выражение:9ab/a+9b×(a/9b-9b/a)= 9(9√8 + 4)(√8 - 4)/(9√8 + 4) + 9(√8 - 4)(9√8 + 4)/(9√8 - 4)= 9((9√8 + 4)(√8 - 4) + (√8 - 4)(9√8 + 4)) / (9√8 + 4)= 9(36 - 32√8 + 36√8 - 16 + 36√8 - 16 + 36 - 16√8) / (9√8 + 4)= 9(56 - 12√8) / (9√8 + 4)= (504 - 108√8) / 9√8 + 4
1)
а) (1/5+8/15)×6 = (3/15 + 8/15) × 6 = (11/15) × 6 = 66/15 = 4.4
б) -13×(-9.3-7.8) = -13×(-17.1) = 219.3
в) 4√5×3√3×√15 = 4√(5×3×15) = 4√(225) = 4×15 = 60
2)
1/5x^2 = -20а) - 1/5x^2+20 = 0
x^2 = 100
x = ±10
б) 1/3x^2-27 = 0
1/3x^2 = 27
x^2 = 81
x = ±9
в) 1/4x^2-4 = 0
1/4x^2 = 4
x^2 = 16
x = ±4
г) x^2+6=5x
x^2 - 5x + 6 = 0
(x - 2)(x - 3) = 0
x = 2 or x = 3
д) x^2-21=4x
x^2 - 4x - 21 = 0
(x - 7)(x + 3) = 0
x = 7 or x = -3
е) x+x/5=-12/5
5x + x = -12
6x = -12
x = -2
ж) x+x/11=24/11
11x + x = 24
12x = 24
x = 2
3) Подставляем a = 9√8 + 4 и b = √8 - 4 в выражение:
9ab/a+9b×(a/9b-9b/a)
= 9(9√8 + 4)(√8 - 4)/(9√8 + 4) + 9(√8 - 4)(9√8 + 4)/(9√8 - 4)
= 9((9√8 + 4)(√8 - 4) + (√8 - 4)(9√8 + 4)) / (9√8 + 4)
= 9(36 - 32√8 + 36√8 - 16 + 36√8 - 16 + 36 - 16√8) / (9√8 + 4)
= 9(56 - 12√8) / (9√8 + 4)
= (504 - 108√8) / 9√8 + 4