An algebra problem by Aly Ahmed
x − 2 + 4 − x + 2 x − 5 = 2 x 2 − 5 x Solve for x .
The answer is 3.
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2 solutions
এই রে! এ আবার কপি করতে শুরু করেছে! স্বভাব না যায় ম'লে :) ওরে, তোরে ভোট দেবে, কান্দিস না।
Same way. I'm glad the answer box tells us to look for an integer! I wonder if there's any way to solve it without that (apart from numerically).
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I tried it by removing the square roots, but got fed up and left. Is there any way to use the form I got, which I have given Chris?
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I haven't found one yet. I guess it's also worth noting that when x = 3 , all the square roots have the same value; but again, I'm not sure how to use this.
Ali Ahmed, will you please post the solution to this problem if you have any?
Since x is expected to be an integer, from 4 − x , we have x ≤ 4 ; and from 2 x − 5 , we have x ≥ 3 . Therefore the possible solutions are x = 3 , 4 . When x = 3 , the equation becomes 1 + 1 + 1 = 2 ( 3 2 ) − 5 ( 3 ) = 3 and holds true. When x = 4 , we have 2 + 0 + 3 = 1 2 . Therefore the solution is x = 3 .
A tricky solution!
For all terms of the given equation to be real, 2 . 5 ≤ x ≤ 4
The answer box indicates that x is an integer.
What remains is to check only two integers, viz. 3 and 4 .
A direct check shows that the answer is 3 . :)
The equation can be rewritten as
x − 2 + 4 − x + 2 x − 5 = 2 ( x − 2 ) ( 2 x − 5 ) + ( 4 − x ) ( 2 x − 5 ) , an interesting form.