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# 2 questions

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1. If a, b, and c are different whole numbers and if a^2+b^2+c^2=90, find the largest possible value of the sum a+b+c.

2. A seven is written at the right end of a 2-digit number to make it a 3-digit number, thereby increasing the value of the 2-digit number by 700. Find the orginial 2-digit number.

Nov 3, 2020

#1
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2. A seven is written at the right end of a 2-digit number to make it a 3-digit number, thereby increasing the value of the 2-digit number by 700. Find the orginial 2-digit number.

Just by visualizing this, I see that the original number was 77.  I don't know how to work problem #1.

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Nov 4, 2020
#2
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1. If a, b, and c are different whole numbers and if a^2+b^2+c^2=90, find the largest possible value of the sum a+b+c.

I have more time now, so I came back to see if I could figure out problem #1.

Since a, b, & c are whole numbers, their squares are likewise whole numbers.

Since a2 + b2 + c2  totals 90, no single one of them can be 90 or larger.

This is a list of the squares less than 90.  What three of them total 90?

1,  4,  9,  16,  25,  36,  49,  64,  81

By brute force I find

1 + 25 + 64   //   sum of square roots is 1 + 5 + 8 = 14

16 + 25 + 49   //   sum of square roots is 4 + 5 + 7 = 16

Those are the only ones, unless I missed one/some.  Check it to see if I overlooked any.  It's very possible.

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Nov 4, 2020