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.

Thanks in advance!

Guest Nov 3, 2020

#1**0 **

*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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Guest Nov 4, 2020

#2**0 **

*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 a^{2} + b^{2} + c^{2} 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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Guest Nov 4, 2020