Question

X в квадрате +14x+48=(x+8)(x+6) докажите торжество

Answer 1

$x^{2}$+14x+48=(x+8)(x+6)
$x^{2}$+14x+48=0
D=$14^{2}$-4*1*48=196-192=4
$\sqrt{D}$=$\sqrt{4}$=2
x1=(-14+2)/2=-6
x2=(-14-2)/2=-8
$x^{2}$+14x+48=(x-x1)*(x-x2)=(x+6)*(x+8)

Answer 2

Factoring the Equation and Proof

To factor the given equation X^2 - 14X - 48 = (X + 8)(X + 6), we can use the method of decomposition. First, we need to find two numbers that multiply to -48 and add to -14. These numbers are -16 and 2. Therefore, we can rewrite the equation as:

X^2 - 14X - 48 = (X^2 - 16X + 2X - 48)

Now, we can factor by grouping:

(X^2 - 16X) + (2X - 48) = X(X - 16) + 2(X - 24)

Now, we can factor out the common terms:

X(X - 16) + 2(X - 24) = (X + 8)(X + 6)

Therefore, we have factored the given equation as (X + 8)(X + 6).

This proves that the given equation X^2 - 14X - 48 = (X + 8)(X + 6).