Question

X^3/4-7X^1/4=0

X square root 3/4 minus 7x square root 1/4 equals 0

Find the real solutions to the equation

Answer 1

Answer on Question #48005 – Math – Algebra

1. $x^{\frac{3}{4}} - 7x^{\frac{1}{4}} = 0$. Find the real solutions to the equation.

Solution.

At first, we will rewrite the initial equation in the next form:

$$x^{\frac{1}{4}}(x^{\frac{1}{2}} - 7) = 0.$$

To satisfy equation, we have

$$x^{\frac{1}{4}} = 0, \text{ hence } x = 0;$$

or

$$\sqrt{x} - 7 = 0,$$

$\sqrt{x} = 7$, hence $x = 49$, because $x$ is non-negative due to the domain of square root.

And finally we obtain $x_1 = 0$, $x_2 = 49$.

Answer:

Real solutions of equation are $x_1 = 0$ and $x_2 = 49$.

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