Ingenious Method for Solving Radical Equations | Math Olympiad

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This math tutorial video shows you some ingenious and cool tricks for solving the radical equation: sqrt(t-1/t)+sqrt(1-1/t)=t. The techniques include difference of squares formula, perfect square formula, quadratic formula.

You are welcome to watch and subscribe to the free math tutoring channel Math Tutoring by Dr. Liang:

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The way of solving this equation is unique.

prabhudasmandal

That was great! Really interesting method of solving.

owlsmath

Nice problem. I did it by moving the “b” part to the right and square both sides, simplify it, then keep the sqrt part one one side and square again, rest is easy.

xyz

Another way is, let √(t--1/t)=a or a^2=t--1/t.and let √(1-1/t)=b or b^2=1--1/t. thus we get a+b=t...(A) and a^2--b^2or putting value of (a+b)=t, we get a--b=(t--1)/t)=(1--1/t).now (A)+(B) gives 2a=t+1--1/t=1+(t--1/t) rearranged to get a^2=(t--1/t).finally, we get a^2--2a+1=0 or (a--1)^2=0 or a=+-1.restoring the value of a we get √(t--1/t)=+-1 or squaring both sides we get t--1/t=1 or t^2--t--1=0 or t=(1+-√(1+4)}/2 or (1+-√5)/2.but (1--√5)/2 being less than 0 is rejected.hence, t= (1+√5)/2 is the answer.

prabhudasmandal

and 1+ sqrt 5
=1.61803
2

devondevon

Ingenious Method for Solving Radical Equations | Math Olympiad

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