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Maths-

General

Easy

Question

Solve the radical equation $cube root of x minus 2 equals 7$ Check for extraneous solutions

hint Hint:

Rearrange the equation and then solve for x.

The correct answer is: x = 729 works

Complete step by step solution:
Here we have the equation $cube root of x minus 2 equals 7$
On rearranging, we have $cube root of x equals 9$
$not stretchy rightwards double arrow x to the power of 1 third end exponent equals 9$
To make the power of the equation as 1, we have to raise the equation by
$not stretchy rightwards double arrow x to the power of 1 third cross times 3 end exponent equals 9 cubed$
⇒ x = 729
On substituting the value of x in the equation, we get
$cube root of 729 minus 2 equals 7$
Hence x = 729 works.
Hence there is no extraneous solution

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