Giải thích các bước giải:
1, x - √x = √x(√x - 1)
2, x - 1 = (√x)² - 1² = (√x +1)(√x - 1)
3, x - 2 = (√x)² - (√2)² =
(√x + √2)(√x - √2)
4, 5 - x = (√5)² - (√x)²
= (√5 + √x)(√5 - √x)
5, x√x - 1 = (√x)³ - 1³
= (√x - 1)[(√x)² + √x . 1 + 1²]
= (√x - 1)(x + √x + 1)
6, 1 + x√x = 1³ + (√x)³
= (1 + √x)[1² - 1 . √x + (√x)²]
= (1 + √x)(1 - √x + x)
7, x√y - y√x = √(xy)(√x - √y)
8, x + 2√x + 1 = (√x)² + 2√x.1 + 1²
= (√x + 1)²
9, 9 - 6√x + x = 3² - 2.3.√x + (√x)²
= (3 - √x)²
10, x√x - y√y = (√x)³ - (√y)³
= (√x - √y)[(√x)² + √x.√y + (√y)²]
= (√x - √y)[x + √(xy) + y]