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Find the real solutions of the equation.
4x^(1/2) - 9x^(1/4) + 4 = 0
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Introduce new variable y = x^(1/4).
Then our original equation takes the form
4y^2 - 9y + 4 = 0.
It is a quadratic equation for y. Solve it using the quadratic formula
= = = .
Thus, there are two real roots for y: y= and y= .
It gives two real positive solutions for x
x = y^4 = = 7.240799963 (approximately).
and
x = y^4 = = 0.138106287 (approximately).
Solved.
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Again, the method of solution is changing the variable.