Answers

1. Answer:

   the roots of the equation are x = 3.6444 and x = -3.6444.

   Step-by-step explanation:

   To solve this equation, we need to find the value of x that makes the equation true.

   First, we can simplify the left side of the equation by combining like terms:

   x² + x(6-2x) = x² – 2x² + 6x = -x² + 6x

   Next, we can simplify the right side of the equation by expanding the product:

   (x-1)(2-x) – 2 = 2x – x – x + 1 – 2 = x – 1 – 2 = -x + -1

   Now that we have simplified both sides of the equation, we can set them equal to each other:

   -x² + 6x = -x + -1

   To solve this equation, we can start by adding x to both sides to get rid of the negative x term on the right side:

   -x² + 6x + x = -x + -1 + x

   This simplifies to:

   -x² + 7x = -1

   Next, we can add 1 to both sides to get rid of the negative 1 on the right side:

   -x² + 7x + 1 = -1 + 1

   This simplifies to:

   -x² + 7x + 1 = 0

   Now we have a quadratic equation in standard form, which we can solve using the quadratic formula:

   x = (-7 +/- sqrt(49 – 4(-1)(1))) / (2(-1))

   Plugging in the values, we get:

   x = (-7 +/- sqrt(49 + 4)) / -2

   This simplifies to:

   x = (-7 +/- sqrt(53)) / -2

   Finally, we can solve for x by finding the square root of 53:

   x = (-7 +/- 7.2887) / -2

   This gives us two solutions:

   x = -7.2887 / -2 = 3.6444

   x = 7.2887 / -2 = -3.6444

   Thus, the roots of the equation are x = 3.6444 and x = -3.6444.

   I hope this helps! Let me know if you have any questions.

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2. Answer:

   -4/3

   Step-by-step explanation:

   given eqn,

   x²+x(6-2x)=(x-1)(2-x)-2

   or,x²+6x-2x²=2x-x²-2+x-2

   or,-x²+6x=3x-4-x²

   or,-x²+x²+6x-3x+4=0

   or,3x+4=0

   or,3x=-4

   or,X=-4/3(which is req. root)

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