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Maths-

General

Easy

Question

Solve the radical equation $13 minus fourth root of x equals 10$ Check for extraneous solutions

hint Hint:

Rearrange the equation and then solve for x.

The correct answer is: x = 81 works

Complete step by step solution:
Here we have the equation $13 minus fourth root of x equals 10$
On rearranging, we have $fourth root of x equals 3$
$not stretchy rightwards double arrow x to the power of 1 fourth end exponent equals 3$
To make the power of the equation as 1, we have to raise the equation by 4
$not stretchy rightwards double arrow x to the power of 1 fourth cross times 4 end exponent equals 3 to the power of 4$
⇒ x = 81
On substituting the value of x in the equation, we get
$13 minus fourth root of 81 equals 13 minus 3 equals 10$
Hence x = 81 works.
Hence there is no extraneous solution.

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