Please help! radical equation

Question

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Is x=18 in the solution set of the radical equation 4 √x-2+4=2 (4 root of x minus 2 end root plus 4 equals 2)? Tell why or why not. Show any work.

Answer 1

Hi Taylor,

 

4sqrt(x - 2) + 4 = 2

4sqrt(x - 2) = -2

sqrt(x - 2) = -1/2

 

There is no real number solution for the above expression. Therefore, x = 18 is not in the solution set.

Answer 2

No.  You can verify this by substituting 18 for x in the equation.  The LHS is 20 when x =18. 

If the RHS is 20, it is OK, but your question shows 2 for the RHS.

 

If the RHS is actually 2, the equation has no solution, and you can state that by observation. The LHS is greater than or equal to 4 since a radical value is non negative.