Math  /  Algebra

Questionx127x14+10=0x^{\frac{1}{2}}-7 x^{\frac{1}{4}}+10=0

Studdy Solution
Verify the solutions by substituting x=16x = 16 and x=625x = 625 back into the original equation.
For x=16x = 16:
x127x14+10=161271614+10=472+10=414+10=0 x^{\frac{1}{2}} - 7x^{\frac{1}{4}} + 10 = 16^{\frac{1}{2}} - 7 \cdot 16^{\frac{1}{4}} + 10 = 4 - 7 \cdot 2 + 10 = 4 - 14 + 10 = 0
For x=625x = 625:
x127x14+10=62512762514+10=2575+10=2535+10=0 x^{\frac{1}{2}} - 7x^{\frac{1}{4}} + 10 = 625^{\frac{1}{2}} - 7 \cdot 625^{\frac{1}{4}} + 10 = 25 - 7 \cdot 5 + 10 = 25 - 35 + 10 = 0
Both values satisfy the original equation. Thus, the solutions are correct.
The solutions are x=16x = 16 and x=625x = 625.

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