Question

A) 4a-a в кубе= b) ax в квадрате+2ax+a

Answer 1

А) 4а-а³=а(4-а²)=а(2-а)(2+а)
б) ах²+2ах+а=а(х²+2х+1)=а((-1)²+2(-1)+1)=а(1-2+1)=а·0=0
Д=4-4=0
х=-2\2=-1

Answer 2

Let's solve each equation step by step:

A) 4a - a³ = b

To solve this equation, we can factor out an 'a' from the left side:

a(4 - a²) = b

Now, we can solve for 'a' by isolating it on one side:

4 - a² = b/a

Next, rearrange the equation:

a² + (b/a) - 4 = 0

To solve this quadratic equation, we can multiply through by 'a' to eliminate the fraction:

a³ + b - 4a = 0

Now, we have a cubic equation in 'a'. Unfortunately, there is no general formula for solving cubic equations like there is for quadratics. However, you can approximate the solutions using numerical methods or use a calculator or computer software to find the roots.

B) ax² + 2ax + a

This is a quadratic equation in 'x'. To solve it, we can factor out the common factor 'a':

a(x² + 2x + 1)

Now, we can see that the quadratic expression inside the parentheses is a perfect square trinomial:

a(x + 1)²

Therefore, the simplified form of the equation is:

a(x + 1)²