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

Algebra.Com
Question 1150463: If x∈Z, what is the sum of the digits of the value x such that √x+⁴√x=30?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!




Introduce a new variable to make it easier to see how to solve the problem.

Let y = x^(1/4)
Then y^2 = x^(1/2)

Then the equation is



or y =

y = -6 gives us x^(1/4) = -6, which is not possible.

y = 5 gives us x^(1/4) = 5, which makes x = 5^4 = 625.

ANSWER: The problem asks for the sum of the digits of x, which is 6+2+5 = 13.

Of course, if a formal algebraic solution is not required, the recognition that x^(1/4) is the square of x^(1/2) means we are looking for two integers, one the square of the other, whose sum is 30. That obviously is 5 and 25, which means x is 5^4 = 35^2 = 625.
Answer by ikleyn(52943)   (Show Source): You can put this solution on YOUR website!
.

The number x itself is 625,


and the sum of its digits (which is under the question) is 6+2+5 = 13.    ANSWER


            ANSWER.  13


RELATED QUESTIONS

If x ∈ ℤ, the sum of the digits of the value of x such that √x + 4√x=30 is: A) (answered by math_tutor2020,MathTherapy)
If the sum of any three consecutive digits is 20, what is the value of... (answered by richard1234)
If x and y are the two digits of 653xy such that the number is divisible by 80, what is... (answered by checkley77)
if 360 = 2^x + 3^y+5^z what is the value of x+y+z... (answered by basketball1127)
If x and y are positive integers such that x=8, what is the maximum possible value of... (answered by Alan3354)
x and 2x are both 3 digit integers. If the sum of the digits of x is 19, what is the sum... (answered by ankor@dixie-net.com)
what's the value of x/5 + 3y^2 - Z if x=30 y=2 z=-2 (answered by vleith)
X-(X*.10)=Z find the value of x if z is the only given number (answered by josgarithmetic)
I have a three digit number such that the sum of the cubes of each digit gives the three (answered by richard1234)