Identify the mistake
Tell me at which step I'm going wrong.
- ( a + 7 ) = 9
- ( a + 7 ) 2 = 8 1
- a 2 + 1 4 a + 4 9 = 8 1
- a 2 + 1 4 a − 3 2 = 0
- a 2 + 1 6 a − 2 a − 3 2 = 0
- a ( a + 1 6 ) − 2 ( a + 1 6 ) = 0
- So, a = − 1 6 and a = 2
- Putting the value of a in our first equation.
- − 1 6 + 7 = 9
How is that possible?
The answer is 8.
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2 solutions
The question was which step is wrong. Step 2 is not wrong in itself in accordance with Step1.
Actualy the question is where you are going wrong not which step is wrong. My modest opinion is that you went wrong with introducing a second solution by squaring step 1 in step 2. This eventualy lead to the wrong substition. But as far as I am concerned I am ok with the correct answer, step 8.
In my opinion step 2 was a bad choice but not wrong. I believe that Step 8 is the wrong one as you should substitute the values of "a" in the quadratic equation of step 2, but not all values of "a" apply to the linear equation of step 1.
* Hint * : If a 2 = 4 9 Is it necessary that? a = 7 If you still don't get it then know that the solutions of a square need not apply on the no.
No it can be -7 also. But how is then the 8 step wrong ?
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Well then you have answered your question yourself. It could be -7 so that means the solutions of ( a + 7 ) 2 = 8 1 may NOT apply on a + 7 = 9 . So putting the values of ( a + 7 ) 2 = 8 1 in a + 7 = 9 was wrong in the first place itself.
In step 2 you introduce the second solution (-16). So I favour step 2 as an answer.