Please have a look at ry1.
The difference of ages does not change .
Suppose we subtract another 25 from it, we get 0 because 25+25 = 50, 50+50=100, 100+100 =200 etc.
Write them under each other, you will soon see that B = 3 or 2 .
This is easier than the previous one. B should be 2 and ...
The 2nd paranthesis is equal to 0 .
ry1 gives the solution .
208 is nearly 225 which is the square of the 15 . So try numbers in the neighborhood of 15.
Think as if the figure is a rectangle; the perimeters are the same .
If a negative number in a negative paranthesis is not treated as a positive number, we lose consistency .
Let the smaller be 1, the second can not be integer. Try the smaller equals 2, the bigger should be 5, the couple does not satisfy the second
condition .
Let the larger be A and smaller B. 2xA = 5xB and 2x(A-B)=12 i.e. A=B+6 . Putting B+6 in the first gives 2xB + 12 = 5xB i.e. B=4
1275 + 225 = ?.
100^{2} - 99^{2} = ?. You can certainly calculate the result.
For a good possible way, have a look at ry1.
1st method to calculate may be the direct method: The sum of the numbers from 1 to 10 is , from nx(n+1)/2 = 5x11 = 55. The first term is
1+4+9+16+25+36+49+64+81+100 = ?
2nd method : For each number 1≤A≤10 A^{2} - A = Ax(A-1) and it is enough to sum these last terms. For A=1 this term vanishes.
The sum of te other terms 2x1+3x2+4x3+5x4+6x5+7x6+8x7+9x8+10x9 = 2x(1+3)+4x(3+5)+6x(5+7)+8x(7+9)+90 = 2x4+4x8+6x12+8x16+90=385 .
Just as in the previous question .
Just make the explicit calculation with the help of a calculator .
Have please a look at ry1 .
2x4+4x8+6x12+8x16+10x20+12x24+14x28+16x32+18x36+380 has all terms as multiples of 4. After we write it in 4x(.+.+....) form, some of the terms
are easily added .
Both of the parenthesis are 100 000 .
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