Greatest Integer Function, Modulus, Roots of an Equation | iTeachChem | Page 1

jolly ivy Dec 2, 2025, 11:16 AM

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How do I even begin?

strong rainBOT Dec 2, 2025, 11:17 AM

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Note for OP

+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.

molten falcon Dec 2, 2025, 1:16 PM

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jolly ivy How do I even begin?

Write out the first eqn. as $x^{2}-11x+31+{x}$

celest sandalBOT Dec 2, 2025, 1:16 PM

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Lance who?

molten falcon Dec 2, 2025, 1:17 PM

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Then solve for x via quadratic equation as $x=\frac{11\pm\sqrt{121-122+4{x}}}{2}$

celest sandalBOT Dec 2, 2025, 1:17 PM

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Lance who?

molten falcon Dec 2, 2025, 1:28 PM

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Okay sorry for disappearing lol, but from here for real roots 4{x}>=1 or {x}>=0.25

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$\text{So expression 'ere}=(5.5\pm\sqrt{{x}-0.25})$

celest sandalBOT Dec 2, 2025, 1:30 PM

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Lance who?

molten falcon Dec 2, 2025, 1:30 PM

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Since {x}-0.25<1, you can find the fractional part and solve forth

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(Making cases where sqrt({x}-0.25)+0.5<1 and >1 and so on

dim remnant Dec 2, 2025, 4:38 PM

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gg lance!

jolly ivy Dec 3, 2025, 1:19 AM

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molten falcon (Making cases where sqrt({x}-0.25)+0.5<1 and >1 and so on

Ohh yes

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thank you 🛐

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+solved @molten falcon

#Greatest Integer Function, Modulus, Roots of an Equation