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It turns out that there are none zero integer (whole numbers with no decimal points) solutions satisfying z? = X+y?, where z is the hypothenuse and x and are the other sides. For example, z= 5, x = 3 and y=4 works because 52 32 + %3D 42. Actually, there are so many other integer solutions to that equation: Try z=10, x=6 and y = 8 1) Give two more integer solutions of the equation z? = +y? · Remember %3D that you are only allowed to work with non-zero integers (whole numbers- no fractions, no decimal point numbers) 2)Now, is it possible to extend the Pythagorean Theorem to the third power to become z? x+y? where z,x and y are whole numbers? In other words, can you find three non-zero integers (z, x and y) satisfying z x3+y?? If so, then you are done from this project. Just write down the integer values of your z, x and y. (To be honest with you, I tried, and I couldn't find any solution). But maybe you are lucky here!

It turns out that there are none zero integer (whole numbers with no decimal points) solutions satisfying z? = X+y?, where z is the hypothenuse and x and are the other sides. For example, z= 5, x = 3 and y=4 works because 52 32 + %3D 42. Actually, there are so many other integer solutions to that equation: Try z=10, x=6 and y = 8 1) Give two more integer solutions of the equation z? = +y? · Remember %3D that you are only allowed to work with non-zero integers (whole numbers- no fractions, no decimal point numbers) 2)Now, is it possible to extend the Pythagorean Theorem to the third power to become z? x+y? where z,x and y are whole numbers? In other words, can you find three non-zero integers (z, x and y) satisfying z x3+y?? If so, then you are done from this project. Just write down the integer values of your z, x and y. (To be honest with you, I tried, and I couldn't find any solution). But maybe you are lucky here!

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter6: Quadratic Equations And Inequalities
Section6.4: Quadratric Formula
Problem 61PS
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It turns out that there are none zero integer (whole numbers with no decimal points) solutions satisfying z? = *+y?, where z is the hypothenuse and x and are the other sides. For example, z= 5, x = 3 and y=4 works because 52 = 32 + 42. Actually, there are so many other integer solutions to that equation: Try z=10, x=6 and y = 8 1) Give two more integer solutions of the equation z? = +y? · Remember %3D that you are only allowed to work with non-zero integers (whole numbers- no fractions, no decimal point numbers) 2)Now, is it possible to extend the Pythagorean Theorem to the third power to become z x+y? where z,x and y are whole numbers? In other words, can you find three non-zero integers (z, x and y) satisfying z x3+y?? If so, then you are done from this project. Just write down the integer values of your z, x and y. (To be honest with you, I tried, and I couldn't find any solution). But maybe you are lucky here!
Transcribed Image Text:It turns out that there are none zero integer (whole numbers with no decimal points) solutions satisfying z? = *+y?, where z is the hypothenuse and x and are the other sides. For example, z= 5, x = 3 and y=4 works because 52 = 32 + 42. Actually, there are so many other integer solutions to that equation: Try z=10, x=6 and y = 8 1) Give two more integer solutions of the equation z? = +y? · Remember %3D that you are only allowed to work with non-zero integers (whole numbers- no fractions, no decimal point numbers) 2)Now, is it possible to extend the Pythagorean Theorem to the third power to become z x+y? where z,x and y are whole numbers? In other words, can you find three non-zero integers (z, x and y) satisfying z x3+y?? If so, then you are done from this project. Just write down the integer values of your z, x and y. (To be honest with you, I tried, and I couldn't find any solution). But maybe you are lucky here!
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