Question

Sa se rezolve ecuatia
2 mx patrat +(1-2m la patrat)x-m=0

Answer 1

2mx² + (1 - 2m²)x - m = 0
Δ=(1 - 2m²)² - 4 × 2m × (-m) = 1 + 4m^4 - 4m² + 8m² = 4m^4 + 4m² + 1 = (2m² + 1)²
x1,2 = [ -(1 - 2m²) +/- |2m² + 1| ] / 4m
Dar 2m² + 1 este intotdeauna pozitiv, deci |2m² + 1| = 2m² + 1

x1 = ( - 1 + 2m + 2m² + 1) / 4m = 2m(m + 1) / 4m = (m + 1) / 2
x2 = ( -1 + 2m - 2m² - 1) / 4m = 2(-m² + m -1) / 4m = (-m² + m - 1)/2m