Michael chose some positive number, multiplied it by itself, added 1, multiplied the result by 10, added 3, and multiplied the r
esult by 4. His final answer was 2012. What number did Michael choose?
1 answer:
Answer: 7
Step-by-step explanation:
Let the number chosen by Michael be x.
We are told that he multiplied it by itself, added 1. This would be:
= = ( x × x) + 1 = x² + 1
We are further told that he multiplied the result by 10, and added 3. This would be:
= = [(x² + 1) × 10] + 3
= 10x² + 10 + 3
= 10x² + 13
Lastly, he multiplied the result by 4 and his final answer was 2012. This would be:
(10x² + 13) × 4 = 2012
40x² + 52 = 2012
40x² = 2012 - 52
40x² = 1960
x² = 1960/40
x² = 49
x = ✓49
x = 7
The number is 7
can be expressed as:
= ( x × x) + 1 = x² + 1
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