Hello and thanks for your question about A^3+B^3=91,
A^2+B^2=25, what is the value of A and B.
I don't know if this question is your homework or not,
but here are some steps to solve your question:
1, according to A^2+B^2=25, we know that A and B must be
between -5 and 5
2, according to A^3+B^3=91 >0, we know A and B must be
greater than 0. Because when raising negative numbers to a
power, if the exponent is an even number, the answer will
always be positive. If the exponent is an odd number, the
answer will always be negative. The above rule is from the
following website:
http://www.kidsonline.net/learn/exp_root/exp_root.html There are more examples of exponents from the following
link:
this website is designed for kids to do some math
practice with a video explaining the exponents:
http://www.homeschoolmath.net/teaching/negative_zero_exponents.php the following link has very clear and easy examples to
help you to understand exponents:
http://www.purplemath.com/modules/negative4.htm 3, therefore A and B are between 0 and 5
4, An odd number plus an odd number is an even number;
an even number plus an odd number is an odd number; an even
number plus an even number is an even number. Therefore we
must choose one odd number and one even number from the set
0, 1, and 2,3,4,5. Here are all the possibilities: 0 and 1;
0 and 3; 0 and 5; 2 and 1; 2 and 3; 2 and 5; 4 and 1; 4 and
3; 4 and 5. One way to find the answer from this point on is
to use trial and error; by trying each of the above sets,
find one that would work for the equation. So for instance,
substitute 0 and 1 into the equation A^2+B^2 to see if the
answer is 25. You will find that there are two sets matching
the equation A^2+B^2=25: they are 0 and 5; 3 and 4. So you
need to try these two sets by using the equation A^3+B^3 to
find which one works for the equation.
When substituting with the terms 3 and 4 into the
equation like so, 3^3+4^3=91, we can see that the equation
is correct. Therefore, we know that the two terms should be
3 and 4.
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