Question

А) 15х2 – 8х + 7 = 0 б) х2 + 8 = 0 в) -28х2 - 18х + 6 = 0 г) 31х + 40 = 0 д) -16х4 + 23 = 0 е) х2 – 2х = 0

Answer 1

Ответ:

Объяснение:

а) 15х² – 8х + 7 = 0;

a=15;  b=-8;  c=7;

Корней нет (D=-356 <0).

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б) х² + 8 = 0 ;

x²=-8;  Квадрат числа не может быть отрицательным

Корней нет.

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в) -28х² - 18х + 6 = 0;

a=-28;  b=-18;  c=6;

x1=-0.884;  x2=0.242.

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г) 31х + 40 = 0;

31x=-40;

x=-40/31.

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д)  ???

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е) х² – 2х = 0;

x(x-2)=0;

x1=0;  x2=2.

Answer 2

Let's solve each of the given equations:

a) 15x^2 - 8x + 7 = 0: To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). For this equation, a = 15, b = -8, and c = 7. Substituting the values into the quadratic formula: x = (-(-8) ± √((-8)^2 - 4 * 15 * 7)) / (2 * 15) x = (8 ± √(64 - 420)) / 30 x = (8 ± √(-356)) / 30 Since the discriminant (√(-356)) is negative, the equation has no real solutions. The solutions would be complex numbers.

b) x^2 + 8 = 0: To solve this quadratic equation, we can subtract 8 from both sides: x^2 = -8 Taking the square root of both sides: x = ±√(-8) Since the square root of a negative number results in a complex number, the equation has no real solutions.

c) -28x^2 - 18x + 6 = 0: Dividing the entire equation by -2: 14x^2 + 9x - 3 = 0 To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). For this equation, a = 14, b = 9, and c = -3. Substituting the values into the quadratic formula: x = (-(9) ± √((9)^2 - 4 * 14 * (-3))) / (2 * 14) x = (-9 ± √(81 + 168)) / 28 x = (-9 ± √(249)) / 28 The solutions can be written as: x = (-9 + √249) / 28 x = (-9 - √249) / 28

d) 31x + 40 = 0: To solve this linear equation, we can subtract 40 from both sides: 31x = -40 Dividing both sides by 31: x = -40/31

e) -16x^4 + 23 = 0: Adding 16x^4 to both sides: 16x^4 = 23 Dividing both sides by 16: x^4 = 23/16 Taking the fourth root of both sides: x = ±√(23/16) x = ±√(23)/√(16) x = ±(√23/4)

So, the solutions to the given equations are: a) No real solutions b) No real solutions c) x = (-9 + √249) / 28, x = (-9 - √249) / 28 d) x = -40/31 e) x = √23/4, x = -√23/4