Решить sqrt (x+5) - sqrt (2x-3) = sqrt (4x-1)

√ (X + 5) - √ (2X - 3) = √ (4X - 1)

(√ X + 5) - √ (2X - 3)) ^2 = (√ 4X - 1) ^2

4X - 1 = (X + 5) + (2X - 3) - 2 * √ (X + 5) * (2X - 3)

4X - 1 = 3X + 2 - 2 √ (2X^2 + 7X - 15)

3X + 2 - 4X + 1 = 2 √ (2X^2 + 7X - 15)

- X + 3 = 2 √ (2X^2 + 7X - 15)

- 0,5X + 1,5 = √ (2X^2 + 7X - 15)

(1,5 - 0,5X) ^2 = (√ 2X^2 + 7X - 15) ^2

2,25 - 1,5X + 0,25X^2 = 2X^2 + 7X - 15

2X^2 - 0,25X^2 + 7X + 1,5X - 15 - 2,25 = 0

1,75X^2 + 8,5X - 17,25 = 0

D = 72,25 + 120,75 = 193

√ D = √ 193 = 5 √ 7,72

X1 = ( - 8,5 + 5 √ 7,72) : 3,5

X2 = ( - 8,5 - 5 √ 7,72) : 3,5