Se o ponto P(x,x) for equidistante dos pontos A(4,8) e B (2,-2), teremos ..
d² = (Px - Ax)² + (Py - Ay)²
d² = (x - 4)² + (x - 8)²
d² = x² - 8x + 16 + x² - 16x + 64
d² = 2x² - 24x + 80
d² = (Px - Bx)² + (Py - By)²
d² = (x - 2)² + (x + 2)²
d² = x² - 4x + 4 + x² + 4x + 4
d² = 2x² + 8
2x² - 24x + 80 = 2x² + 8
24x = 72
x = 3
pronto
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Verified answer
d² = (Px - Ax)² + (Py - Ay)²
d² = (x - 4)² + (x - 8)²
d² = x² - 8x + 16 + x² - 16x + 64
d² = 2x² - 24x + 80
d² = (Px - Bx)² + (Py - By)²
d² = (x - 2)² + (x + 2)²
d² = x² - 4x + 4 + x² + 4x + 4
d² = 2x² + 8
2x² - 24x + 80 = 2x² + 8
24x = 72
x = 3
pronto