For what values does the sqr root of 2x = x square root 2 ?
Square both sides.
It solves very nicely to x=0 or x=1
To find the values for which the square root of 2x is equal to x multiplied by the square root of 2, we need to solve the equation:
√(2x) = x√2
To do this, we can square both sides of the equation, keeping in mind that squaring both sides can introduce extraneous solutions:
(√(2x))^2 = (x√2)^2
Simplifying both sides of the equation, we get:
2x = 2x^2
Rearranging this equation, we get a quadratic equation:
2x^2 - 2x = 0
Factoring the equation, we get:
2x(x - 1) = 0
Now, we can apply the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must equal zero. So, we set each factor equal to zero and solve for x:
2x = 0 -> x = 0
x - 1 = 0 -> x = 1
Therefore, the values for which the square root of 2x is equal to x multiplied by the square root of 2 are x = 0 and x = 1.