Question

Solve for (a+1)/2=1/a.

Answer 1

Hello!

To solve this, you are trying to convert one side to a quadratic equation and the other to just 0. Then, solve the equation.

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First, move the /2 to the other side of the equation.

(a+1)/2 = 1/a

a+1 = 2/a

Next, multiply both sides by a.

a+1 = 2/a

$a^{2} +a=2$

And then subtract both sides by 2. This will get you to a quadratic equation.

$a^{2} +a=2$

$a^{2} +a-2=0$

Now, factor the equation. When we're factoring, we are looking for the form (a + b)(a + c), where b + c must equal 1 (the coefficient of a) and b*c must equal -2. In this case, b = 2, and c = -1.

Therefore:

$a^{2} +a-2=0$

(a + 2)(a - 1) = 0

To get the answer, recall that anything multiplied by 0 is equal to 0. Therefore, to get the left side to equal 0, either (a + 2) or (a - 1) must equal 0. To do this, a must either be -2 or 1.

Therefore, a = -2, or a = 1.

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Check your work:

(-2 + 1)/2 = 1/-2

-1/2 = -1/2

(1 + 1)/2 = 1/1

2/2 = 1/1

1 = 1

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Hope this helps!