Question 1182754: If x^2=x+3, then x^3 equals
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
If x^2=x+3, then x^3 equals
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There are two strategies to solve this problem.
First strategy is to write the given equation in the form
x^2 - x - 3 = 0,
then apply the quadratic formula
 =  =  . (1)
And then to raise it to the degree 3.
At this point, it becomes clear that, rising this expression to the degree 3, it is not very pleasant or very smart strategy.
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| So, I will show you ANOTHER strategy. |
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From x^2 = x+3, you have x^3 = x*x^2 = replace x^2 by x+3, as it is given, and get = x*(x+3) = x^2 + 3x =
= replace x^2 by x+3 a g a i n = (x+3) + 3x = 4x + 3.
Now substitute (1) into the last expression and get
x^3 =  =  + 3 =  . ANSWER
Solved.
Thus you have two expressions for x^3 : It is  or  .
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comment from student: Hi, thank you for your help but the correct answer is 4x+3.
May I know is there a way to get to this answer?
My response. Sure.
This answer 4x+3 is an INTERMEDIATE expression in my solution.
Find it in my post : for it, READ it ATTENTIVELY.
Simply, in my solution, I came FURTHER than that expression and provided the final numerical value/values.
Answer by greenestamps(13200)  (Show Source):
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