Question

Докажите тождество a)2а-3b=-(3b-2a) б)(3с-4d)²=(4d-3c)² ПРОШУ И УМОЛЯЮЮЮ

Answer 1

А) 2a-3b=-(-2a+3b)=-(3b-2a)

б) (3c-4d)²=(3c-4d)(3c-4d)=(-1)*(-3c+4d)*(-1)*(-3c+4d)=(-1)*(-1)(4d-3с)(4d-3с)=(4d-3с)(4d-3с)=(4d-3с)²

или второй вариант б)

(3c-4d)²=(-(-3c+4d))²=(-1)²*(4d-3с)²=(4d-3с)²

Answer 2

a) To prove the identity 2a - 3b = -(3b - 2a), we can start by simplifying both sides of the equation.

On the left side, we have 2a - 3b.

On the right side, we have -(3b - 2a). To simplify this, we can distribute the negative sign to both terms inside the parentheses, which gives us -3b + 2a.

Now, we can compare the left and right sides of the equation:

2a - 3b = -3b + 2a

We can see that both sides are equal. Therefore, the identity is true.

b) To prove the identity (3c - 4d)² = (4d - 3c)², we can start by expanding both sides of the equation.

On the left side, we have (3c - 4d)². This can be expanded as (3c - 4d) * (3c - 4d), which gives us 9c² - 12cd - 12cd + 16d², or 9c² - 24cd + 16d².

On the right side, we have (4d - 3c)². This can be expanded as (4d - 3c) * (4d - 3c), which gives us 16d² - 12cd - 12cd + 9c², or 16d² - 24cd + 9c².

Now, we can compare the expanded forms of both sides of the equation:

9c² - 24cd + 16d² = 16d² - 24cd + 9c²

We can see that both sides are equal. Therefore, the identity is true.

In conclusion, we have proved both identities:

a) 2a - 3b = -(3b - 2a) b) (3c - 4d)² = (4d - 3c)²