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!
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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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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