Math Olympiad || A Nice Irrational Equation || Find x

#matholympiad #irrationalequation #squareroot #olympiad

Hello Genius 👋
Hope you all are doing well 😊

Today we learn about irrational equation.
Irrational Equation are those where the variable is inside the radical that is the reason irrational equation is also known as Radical Equation.

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Do you know what is reciprocal equation??

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[mohamedmnasria]

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[ganda]

√(x-2)^2=(8-x)^2
x-2=x^2-16x+64
x^2-17x+66
(x-6)(x-11)
x=6 dan x=11

[hasobehencho.]

Only 6 will be the answer 11 not possible

[moeberry]

Do not make a math channel when you don’t know what your talking about, first of all the sqrt(x-2) is always nonnegative which means also 8-x has to be greater than or equal to 0. And x-2 must be greater than or equal to 0 since it is the domain of the sqrt(x-2). Putting these together we have x between 2 and 8 inclusive. Therefore x=11 is impossible and x=6 is the only solution. You got x=11 from squaring both sides and not paying attention to the extraneous solution.