Answer to Question #3632 in Algebra for murni

Question

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

Answer 1

These equation can be rewritten in such form:(3x+y+1)/8 = (x-y)/5 AND (x - y) / 5 = (x² - y²) / 5From the first equation: y = (7x + 5) / -7
After substituting into the second equation, we have:
x + (7x + 5) / -7 = x² - ((7x + 5) / -7)²12x² - 19x - 4 = 0D = 361 + 192 = 553
x₁ = (19 + √(553)) / 24, x₂ = (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