Question

1) 6\(x+1)(x+2)+8\(x-1)(x+4)=1 2) x\x-3+4\x+3=18\x^2-9 3)15- (2x-4-3x\5)=7x- x-7\2-5x 4)x^6-19x^3-216=0 5)x^4-y^4\4x^2-2x+y-y^2:x^3-x^2y+xy^2-y^3\2x-y

Answer 1

V-это корень
1)(x+1)*(x+2) = x^2 +3x+2;
(x-1)*(x+4) = x^2+3x - 4;
x^2 + 3x = y;
(6/(y+2)) + (8/(y-4)) = 1;
y не=-2 и y не=4;
6*(y-4) + 8*(y+2) = (y+2)*(y-4);
6y-24 + 8y +16 = y^2 - 2y -8;
y^2 -y*(2+8+6) - 8 + 24 -16 = 0;
y^2 - 16y =0;
y*(y-16) = 0;
y=0 или y-16=0;
1) y=0; <=> x^2+3x = 0; <=> x*(x+3) = 0; <=> x1=0; или x2=-3.
2) y-16 = 0; <=> x^2+3x - 16 = 0;
D = 3^2 + 4*16 = 9+64 = 73;
x3 = (-3+(V73))/2;
x4 = (-3-(V73))/2.
2)на фото
ну наверное так

Answer 2

1. To solve this equation, we will first simplify the expressions on both sides: 6(x+1)(x+2)+8(x-1)(x+4)=1 (6/(x+1)(x+2)) + (8/(x-1)(x+4)) = 1 Now we can multiply both sides by the denominators to eliminate them from the equation: 6(x-1)(x+4) + 8(x+1)(x+2) = (x+1)(x+2)(x-1)(x+4) Expanding both sides: 6x^2 + 8x + 72 + 8x^2 + 24x + 16 = x^4 + 6x^3 - 13x^2 - 108x - 72 Bringing all the terms to one side: x^4 + 6x^3 - 13x^2 - 122x - 160 = 0 This is a fourth-degree polynomial equation. There is no general formula to solve equations of degree higher than 2, but we can use numerical methods or approximation techniques to find the roots. One way to do this is to use the rational root theorem to find possible rational roots and then use synthetic division to test them. We can also use graphical methods or software programs to find the roots.

2. To solve this equation, we will first simplify the expressions on both sides: x/(x-3) + 4/(x+3) = 18x^2 - 9 Multiplying both sides by the common denominator (x-3)(x+3): x(x+3) + 4(x-3) = (18x^2 - 9)(x-3)(x+3) Expanding both sides: x^2 + 3x + 4x - 12 = 18x^2(x-3) - 9(x-3)(x+3) Simplifying: x^2 + 7x - 12 = 9x^3 - 81x Bringing all the terms to one side: 9x^3 - 81x - x^2 - 7x + 12 = 0 This is a cubic equation. There are various methods to solve cubic equations, including factoring, using the rational root theorem, or using the cubic formula. In this case, we can factor out (x-3) as a factor to simplify the equation and then use either synthetic division or the quadratic formula to find the remaining roots.

3. To solve this equation, we will first simplify the expression on the left-hand side: 15 - (2x-4-3x/5) = 7x - x - 7/2 - 5x 15 - (7x/5 - 4) = x - 7/2 - 3x Multiplying both sides by 10 to eliminate the fractions: 150 - 14x = 20x - 35 - 30x Combining like terms: 16x = 115 Dividing both sides by 16: x = 115/16 This is the solution to the equation.

4. To solve this equation, we can use a substitution u = x^3. Then the equation becomes: u^2 - 19u - 216 = 0 This is a quadratic equation in u. We can use the quadratic formula to find the roots: u = (19 ± sqrt(19^2 + 4*216))/2 u = (19 ± 25)/2 u1 = 22, u2 = -3