SOLUTION: Let x spadesuit y = x^2/y for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that a spadesuit a + 1 = 9. Write your answer as a list separated by commas.

Algebra ->  Functions -> SOLUTION: Let x spadesuit y = x^2/y for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that a spadesuit a + 1 = 9. Write your answer as a list separated by commas.      Log On


   



Question 1209325: Let x spadesuit y = x^2/y for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that a spadesuit a + 1 = 9. Write your answer as a list separated by commas.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Let x spadesuit y = x^2/y for all x and y such that y =/= 0.
Find all values of "a" such that "a" spadesuit a + 1 = 9.
Write your answer as a list separated by commas.
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        As written in the post, this formulation is ambiguous.

        It depends on how to read this passage  "a spadesuit a + 1 = 9".

        I will solve the problem reading it as  "a spadesuit (a+1) = 9".

        Another possible reading is  "(a spadesuit a) + 1 = 9".


        As the post is presented, it is clear that it is unprofessional writing.


Following the definition of the term "x spadesuit y", given in the first sentence,
I interpret the second sentence as an invitation to solve this equation

    a%5E2%2F%28a%2B1%29 = 9  in the domain  a =/= -1.


It reduces to 

    a^2 = 9(a+1),

    a^2 - 9a - 9 = 0,

    a%5B1%2C2%5D = %289+%2B-+sqrt%28%28-9%29%5E2+-+4%2A1%2A%28-9%29%29%29%2F%282%2A1%29 = %289+%2B-+sqrt%28117%29%29%2F2.


ANSWER.  There are two solutions for "a".  

         They are  a%5B1%5D = %289+-+sqrt%28117%29%29%2F2  and  a%5B1%5D = %289+%2B+sqrt%28117%29%29%2F2.

Solved.