Question #3632

Find all pairs of value of x and y such that
(3x+y+1)/8 = (x-y)/5 = (x[sup]2[/sup]-y[sup]2[/sup])/5

Expert's answer

These equation can be rewritten in such form:(3x+y+1)/8 = (x-y)/5 AND (x - y) / 5 = (x^{2} - y^{2}) / 5From the first equation: y = (7x + 5) / -7

After substituting into the second equation, we have:

x + (7x + 5) / -7 = x^{2} - ((7x + 5) / -7)^{2}12x^{2} - 19x - 4 = 0D = 361 + 192 = 553

x_{1} = (19 + √(553)) / 24, x_{2} = (19 - sqrt(553)) / 24so, we have such pairs:

1) x = (19 + √(553)) / 24 AND y = (7*(19 + √(553)) / 24 + 5) / -7

2) y = (19 - √(553)) / 24 AND y = (7*(19 - √(553)) / 24 + 5) / -7

After substituting into the second equation, we have:

x + (7x + 5) / -7 = x

x

1) x = (19 + √(553)) / 24 AND y = (7*(19 + √(553)) / 24 + 5) / -7

2) y = (19 - √(553)) / 24 AND y = (7*(19 - √(553)) / 24 + 5) / -7

## Comments

## Leave a comment