SOLUTION: 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

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
Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

sqrt(x) + fourthRoot(x) = 30
x^(1/2) + x^(1/4) = 30
x^(2/4) + x^(1/4) = 30
(x^(1/4))^2 + x^(1/4) = 30
(w)^2 + w = 30 .... let w = x^(1/4)
w^2+w-30 = 0
(w+6)(w-5) = 0
w+6 = 0 or w-5 = 0
w = -6 or w = 5

Since w = x^(1/4), this means x = w^4
Regardless of what w is, the value of w^4 will never be negative, assuming w is a real number.
You can think of w^4 as (w^2)^2 and note how w^2 is never negative.
So we can ignore w = -6 because this is extraneous.

If w = 5, then,
x = w^4
x = 5^4
x = 625

Adding the digits of this x value leads to 6+2+5 = 12

Answer: B) 12

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

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

OR
Other option is to substitute a NEW variable for , solve for that variable, and then BACK-SUBSTITUTE the value to get the value of x.
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