Question

A binary operation * is defined as the set of real numbers by a * b = a/b + b/a where a and b belong to R. Simplify (x + 1) * 2=3

Answer 1

In the above question, what happened to 3

Answer 2

Good question, Kenny
Explanation: the bot messed up again
should be ...

(x + 1) * 2 = 3
(x+1)/2 + 2/(x+1) = 3
times 2(x+1)
(x+1)^2 + 4 = 6(x+1)
x^2 + 2x + 1 + 4 = 6x + 6
x^2 - 4x -1 = 0
x = 2+√5 or x = 2-√5

Answer 3

To simplify (x+1)*2 = 3, we substitute a= x+1 and b=2 in the definition of the binary operation:

a * b = a/b + b/a

(x+1) * 2 = (x+1)/2 + 2/(x+1)

Multiplying both sides by the common denominator 2(x+1), we get:

2(x+1) * (x+1) + 4 = (x+1)^2 + 4(2)

Expanding and simplifying:

2x^2 + 6x - 1 = 0

Using the quadratic formula:

x = [-6 ± sqrt(6^2-4(2)(-1))] / (2(2))

x = (-3 ± sqrt(7))/2

Therefore, (x+1)*2 = 3 is equivalent to x = (-3 ± sqrt(7))/2.

Answer 4

In the given equation, (x+1)*2 = 3, the number 3 represents the value to which the expression (x+1)*2 is being equated. We have to solve for the value of x that satisfies this equation. Once we find the value of x, we can substitute it back into the equation to verify that it indeed satisfies the equation.

So, we did not eliminate the number 3. Instead, we manipulated the equation using the definition of the binary operation to find the solution for x.

Answer 5

Thank you for bringing this to my attention. I apologize for the error in my previous response. You are correct in that the correct solution to the equation (x+1)*2=3 is x = 2+√5 or x = 2-√5, which was obtained by manipulating the equation using the definition of the binary operation and solving the resulting quadratic equation.