Question 1171818

If x ∈ ℤ, the sum of the digits of the value of x such that √x + 4√x=30 is:

A) 11
B) 12
C) 13
D) 14
E) 15

https://ibb.co/fdN00HJ
<pre>{{{matrix(5,3, sqrt(x) + root(4, x), "=", 30, x^(1/2) + x^(1/4), "=", 30, x^(1/2) + x^(1/4) - 30, "=", 0, (x^(1/4))^2 + x^(1/4) - 30, "=", 0, (x^(1/4) - 5)(x^(1/4) + 6), "=", 0)}}}
{{{matrix(1,2, matrix(2,1, "", x^(1/4)), matrix(1,7, - 5, "=", 0, OR, x^(1/4) + 6, "=", 0))}}}
{{{matrix(1,2, matrix(2,1, " ", x^(1/4)), matrix(1,7, "=", 5, OR, x^(1/4), "=", - 6, "(ignore)"))}}}
{{{matrix(1,7, (x^(1/4))^4, "=", 5^4, "=====>", x, "=", 625)}}}
{{{highlight_green(matrix(1,6, Sum, of, "digits:", 13, "(CHOICE", "C)"))}}}
OR
Other option is to substitute a NEW variable for {{{matrix(2,1, " ", x^(1/4))}}}, solve for that variable, and then BACK-SUBSTITUTE the value to get the value of x.