Question

1) х в 2 степени + 6х + 9 = 2) у в 4 степени - у в 3 степени =3) 15а в 3 степени - 5 а =4) а в 7 степени - 3а в 5 степени =​

Answer 1

1) x²+6x+9=(x+3)²

2)y⁴-y³=y³(y-1)

3)15a³-5a=5a(3a²-1)

4)a^7 -3a^5=a^5(a²-3)

Answer 2

1. To solve the equation х^2 + 6х + 9 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 1, b = 6, and c = 9. Plugging these values into the quadratic formula, we get:

x = (-6 ± √(6^2 - 4(1)(9))) / (2(1))

Simplifying further:

x = (-6 ± √(36 - 36)) / 2

Since the discriminant (b^2 - 4ac) is zero, both solutions will be the same. Evaluating the expression, we have:

x = (-6 ± √0) / 2 x = -6 / 2 x = -3

Therefore, the solution to the equation х^2 + 6х + 9 = 0 is x = -3.

2. To solve the equation у^4 - у^3 = 0, we can factor out у^3 from both terms:

у^3(у - 1) = 0

This equation will be true if either у^3 = 0 or (у - 1) = 0.

For у^3 = 0, the only solution is у = 0.

For (у - 1) = 0, we have у = 1.

Therefore, the solutions to the equation у^4 - у^3 = 0 are у = 0 and у = 1.

3. To solve the equation 15а^3 - 5а = 0, we can factor out 5a from both terms:

5a(3a^2 - 1) = 0

This equation will be true if either 5a = 0 or (3a^2 - 1) = 0.

For 5a = 0, the solution is a = 0.

For (3a^2 - 1) = 0, we can add 1 to both sides and then divide by 3 to isolate a^2:

3a^2 = 1 a^2 = 1/3

Taking the square root of both sides, we have:

a = ±√(1/3)

Therefore, the solutions to the equation 15а^3 - 5а = 0 are a = 0, a = √(1/3), and a = -√(1/3).

4. To solve the equation а^7 - 3а^5 = 0, we can factor out а^5 from both terms:

а^5(а^2 - 3) = 0

This equation will be true if either а^5 = 0 or (а^2 - 3) = 0.

For а^5 = 0, the solution is а = 0.

For (а^2 - 3) = 0, we can add 3 to both sides and then take the square root to isolate a:

а^2 = 3 a = ±√3

Therefore, the solutions to the equation а^7 - 3а^5 = 0 are a = 0, a = √3, and a = -√3.