Prove that there are no solutions in integers x and y to the equation 2x^2 + 5y^2 = 14

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blythephillips1867 blythephillips1867

04-02-2018
Mathematics

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Prove that there are no solutions in integers x and y to the equation 2x^2 + 5y^2 = 14

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Classic61l Classic61l · Answer 1 · 2018-02-04T10:15:11+01:00

Classic61l Classic61l

04-02-2018

Solve the equation for y using the formula for slope: y + mx + b

2x^2 + 5y^2 = 14
5y^2 = -2x^2 + 14
y^2 = -2/5x^2 + 14/5
y = the sq root of -2x^2/5 + 14/5

There is no integer solution to the square root of a negative number.

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