2 and -2 both are the solution of the equation x/2 = 2/x.
According to the given question.
We have an equation 2/x = x/2.
As we know that, as we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.
Therefore, the solution of the equation 2/x = x/2 is given by
2/x = x/2
⇒ 2 = (x/2)x (multiplying both the sides by x)
⇒ 2 = x^2/2
⇒ 2(2) = x^2 (multiplying by 2 both the sides by 2)
⇒ 4 = x^2
⇒ x^2 = 4
⇒ x = √4
⇒ x = ±2
⇒ x = 2 or -2
Now we will check 2 is the solution of the given equation or not.
Therefore,
LHS = 2/2 = 1
RHS = 2/2 = 1
Here, LHS = RHS. Therefore, 2 is the solution of the given equation.
Similarly, for -2
LHS = 2/-2 = -1
RHS = -2/2 = -1
Here. RHS = LHS. Therefore, -2 is also the solution of the given equation.
Hence, 2 and -2 both are the solution of the equation x/2 = 2/x.
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