Number Sense Problems

[kd9485]

I have a few problems that I don't really know how to do. Could someone explain how to do these?

72^2 + 13^2 = ___. (5353)

If x + y = 5 and xy = 1 then x^3 + y^3 = ____. (110)

45^2 + 46^2 = ____. (4141)

If f(x) = (2x+1)/(3x+4), then f`(-1) = ____. (5)

[kd9485]

I figured out the last one.

If f(x) = (ax+b)/(cx+d), then f'(x) = (ad-bc)/(cx+d)^2.

[michel470]

72^2 + 13^2 = ___. (5353)
45^2 + 46^2 = ____. (4141)
These are the same type of problems. Notice that the outer digits( 7 and 3, 4 and 6) add up to ten, and the inside digits(2 and 1, 5 and 4) differ by one. Whenever that happens, all you have to do is grab the first number(ex: 72), square each of its digits(7^2=49, 2^2=4), add them together(49+4=53), and multiply by 11(53*101=5353).

If x + y = 5 and xy = 1 then x^3 + y^3 = ____. (110)
Square the (x+y), subtract 3xy's, and multiply by (x+y)
5^2=25-3(1)=22*5=110
If by chance they give you x-y instead of x+y, follow the same procedure except ADD 3xy's instead of subtracting

[nsguy1350]

Yes, basically, [unparseable or potentially dangerous latex formula], and
[unparseable or potentially dangerous latex formula]
Just remember that adding x and y means to subtract the 3 term, and subtracting x and y means adding the 3 term.
Everything is covered.

Also, one last note;
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This is basically LaTeX form of what the above people said.
Watch out for negative signs and subtracting negatives on the derivative one!