300 Followers problem (Not the old one)
x − 2 = 4 − 3 4 − 3 1 0 − 3 x , x = ?
The answer is 3.
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4 solutions
Why should it be a perfect square?
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Good point. I just assumed it was, but you're right it wouldn't have to be.
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By solving the quadratic that results your realize it is a perfect square.
x − 2 = 4 − 3 4 − 3 1 0 − 3 x
Let f ( x ) = 4 − 3 x . Equation is f ( f ( f ( x − 2 ) ) ) = x − 2 .
Since f ( x ) is continuous decreasing over its domain, so is f ( f ( f ( x ) ) ) .
So, f ( f ( f ( x ) ) ) = x at most one real root (continuous decreasing in LHS and increasing in RHS).
And, since 1 is trivially a solution of f ( x ) = x , it is a solution if f ( f ( f ( x ) ) ) = x
Thus, the unique solution is x = 3
Just do, √4-3 = √1 = 1. Then: x - 2 = √10 - 3x, (x-2)² = (√10-3x)², x² - x - 6 = 0, x' = 3, x" = -2.
Someone plz solve this:In triangle ABC,Angles are in g.p.(A,B,C) with common ratio 2, then find 1/b+1/c-1/a.
lol post this as a note sir.
Hi karan as the values of a, b and c are in gp with a cratio of 2 we can write b and c as 2a and 4a. The sum of angles in a triangle is 180 so the value of a is 25.71, b is 51.43 and c is 102.86. From these three values u can find the value of the required expression
It can be seen that x − 2 must be positive, as n returns a positive value or zero. Therefore x > = 2 . And 1 0 − 3 x > = 0 to avoid imaginary numbers and must be a perfect square. From this, x must be 1, 2, or 3. Of these, only 3 satisfies all conditions.