Question

(x²+14x+14)(x²+x+14)=14x²

Answer 1

$( {x}^{2} + 14x + 14)( {x}^{2} + x + 14) = 14 {x}^{2}$

Сделаем замену: х² + 14 = t , t ≥ 0

( t + 14x )( t + x ) = 14x²

t² + tx + 14tx + 14x² = 14x²

t² + 15tx = 0

t × ( t + 15x ) = 0

1 ) t = 0

x² + 14 = 0

x² = - 14

Не имеет действительных корней ( ∅ )


2) t + 15x = 0

t = - 15x

x² + 14 = - 15x

x² + 15х + 14 = 0

х = - 1 ; - 14


ОТВЕТ: - 1 ; - 14

Answer 2

решение на фото внизу

Answer 3

Let's check if the given equation is true:

(x² + 14x + 14)(x² + x + 14) = 14x²

To verify this, we'll start by expanding the left-hand side (LHS) of the equation:

(x² + 14x + 14)(x² + x + 14) = x²(x² + x + 14) + 14x(x² + x + 14) + 14(x² + x + 14) = x⁴ + x³ + 14x² + 14x² + 14x + 14x + 196 = x⁴ + x³ + 28x² + 28x + 196

Now let's simplify the right-hand side (RHS) of the equation:

14x²

Since the highest degree of x on the LHS is x⁴ (due to x⁴ term), and the highest degree of x on the RHS is ² (due to 14x² term), it's apparent that these two expressions are not equal.

Hence, the given equation is not true:

(x² + 14x + 14)(x² + x + 14) ≠ 14x²