Question

При каком значении K трёхчлен K-50b+b² можно представить в виде квадрата дчкчлена​

Answer 1

Ответ:

В решении.

Объяснение:

При каком значении K трёхчлен K-50b+b² можно представить в виде квадрата двучлена?

​K - 50b + b²;

Развёрнута формула квадрата разности:

(а - в)² = а² - 2ав + в²;

2ав = 50b = 2*а*b

а = 50b/2b

a = 25, значит, К = 25²;

К = 625;

Проверка:

(25 - b)² = 25² - 2*25*b + b² = 625 - 50b + b², верно.

Answer 2

Finding the Value of K in the Quadratic Expression

To find the value of K in the quadratic expression K - 50b + b² that allows it to be represented as a square of a binomial, we can use the process of completing the square.

First, let's rewrite the given expression in the form of a perfect square trinomial:

K - 50b + b²

To complete the square, we need to add and subtract a constant term inside the parentheses. The constant term we add and subtract is half the coefficient of the linear term squared.

The linear term in the given expression is -50b, so the constant term we add and subtract is (-50/2)² = (-25)² = 625.

Now, we rewrite the expression by adding and subtracting 625:

K - 50b + 625 - 625 + b²

This can be simplified to:

(b - 25)² + (K - 625)

From this, we can see that the given expression can be represented as a square of a binomial (b - 25) if K - 625 = 0.

Therefore, the value of K that allows the expression K - 50b + b² to be represented as a square of a binomial is K = 625.