Solve for X SURD expression

Question

Solve for X given that:

X = 2a/b = b/(a/2)

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Answer 1

At first sight, this seems like a problem with three unknown variables and not enough equations to solve for them, but there is a way to simplify!

Let's consider the two latter thirds of the expression: 2a/b=b/(a/2). Let's first rearrange the right side of the equals sign by taking the fraction a/2 out from the denominator. We could rewrite our equation as follows now:

2a/b=(b/1)*(2/a)

Combining the parentheses we get:

2a/b=2b/a

or after simplifying:

a/b=b/a

and by multiplying by both a and b on both sides of the equals sign we could rearrange the equation as:

a²=b²

or

a=±b

This provides two different solutions. if we plug in a=b back into our original equation, we will get x=2. If we plug in a=-b, we would get x=−2

Therefore, the two valid answers would be x=±2