How would I solve:
X^(4/3)+X^(2/3)=28
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solve x^(4/3)+x^(2/3)=28
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let x^(2/3) = y
then we have
y^2 + y - 28 = 0
y = (-1 ± √113)/2
so x^(2/3) = (1+√113)/2
x = [(1 + √113)/2]^(3/2) = appr. 10.566
or x^(2/3) = (-1 - √113)/2 , which has no solution
To solve the equation X^(4/3) + X^(2/3) = 28, we can follow these steps:
Step 1: Rewrite the equation using a common denominator for the exponents.
X^(4/3) + X^(2/3) = 28
(X^(4/3))*(X^(2/3)) + X^(2/3) = 28
Step 2: Combine the terms with the same exponent.
X^(4/3 + 2/3) + X^(2/3) = 28
X^(6/3) + X^(2/3) = 28
X^2 + X^(2/3) = 28
Step 3: Substitute X^(2/3) with a new variable to simplify the equation further. Let's say we substitute X^(2/3) = Y.
X^2 + Y = 28
Step 4: Rearrange the equation to solve for X^2.
X^2 = 28 - Y
Step 5: Solve for X by taking the square root of both sides of the equation.
X = ± √(28 - Y)
Step 6: Substitute Y back in terms of X^(2/3).
X = ± √(28 - X^(2/3))
By following these steps, you should be able to find the solutions for the equation X^(4/3) + X^(2/3) = 28.