Question

(x-2)^2×(x-3)=12×(x-2)

Answer 1

Ответ:

x(2)=2

x(1)=-1

x(3)=6

Пошаговое объяснение:

(x-2)²×(x-3)=12×(x-2)

(x-2)²×(x-3)-12(x-2)=0

(x-2)×((x-2)×(x-3)-12)=0

(x-2)×(x²-3x-2x+6-12)=0

(x-2)×(x²-5x-6)=0

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x-2=0

x²-5x-6=0

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x-2=0

x=2

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x²-5x-6=0

x²+x-6x-6=0

x×(x+1)-6(x+1)=0

(x+1)×(x-6)

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x+1=0

x=-1

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x-6=0

x=6

Answer 2

To solve the given equation $(x-2)^2 \cdot (x-3) = 12 \cdot (x-2)$, follow these steps:

Step 1: Expand both sides of the equation: $(x-2)^2 \cdot (x-3) = 12 \cdot (x-2)$ $(x^2 - 4x + 4) \cdot (x-3) = 12x - 24$

Step 2: Distribute the terms on the left side: $x^3 - 3x^2 - 4x^2 + 12x + 4x - 12 = 12x - 24$ $x^3 - 7x^2 + 16x - 12 = 12x - 24$

Step 3: Subtract $12x$ from both sides: $x^3 - 7x^2 + 16x - 12 - 12x = -24$ $x^3 - 7x^2 + 4x - 12 = -24$

Step 4: Add $24$ to both sides: $x^3 - 7x^2 + 4x - 12 + 24 = 0$ $x^3 - 7x^2 + 4x + 12 = 0$

The equation is now in the standard form of a cubic equation. At this point, you can attempt to factor the cubic equation or use numerical methods to approximate the solutions. If you're looking for exact solutions, you might need to use more advanced techniques like the Rational Root Theorem or the cubic formula. If you're looking for approximate solutions, you can use numerical methods like the Newton-Raphson method or graphing software to find the roots.