The value of k is -11.
Given
The equation 3√(x-k)-2=10 has a solution of x = 5.
To find the value of k put x = 5 in the equation then solve for the value of k.
Therefore,
The value of k is;
[tex]\rm 3\sqrt{x-k}-2=10[/tex]
Substitute x = 5 in the equation
[tex]\rm 3\sqrt{5-k}-2=10\\\\\rm 3\sqrt{5-k}=10+2\\\\\rm 3\sqrt{5-k}=12\\\\\rm \sqrt{5-k}=\dfrac{12}{3}\\\\ \sqrt{5-k}=4\\\\[/tex]
Squaring on both sides
[tex]\rm \sqrt{5-k}=\dfrac{12}{3}\\\\5-k=16\\\\-k = 16-5\\\\-k=11\\\\k=-11[/tex]
Hence, the value of k is -11.
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