展开 sqrt(33-12\sqrt{6)}

解答

展开

33 - 126

26 - 3

十进制

1.89897 \dots

求解步骤

33 - 126

= 24 - 126 + 9

= 4 \cdot 6 - 126 + 9

= (4)^{2} (6)^{2} - 126 + (9)^{2}

4 = 2

9 = 3

= 2^{2} (6)^{2} - 126 + 3^{2}

2 \cdot 26 \cdot 3 = 126

= (26)^{2} - 2 \cdot 26 \cdot 3 + 3^{2}

使用完全平方公式:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(26)^{2} - 2 \cdot 26 \cdot 3 + 3^{2} = (26 - 3)^{2}

= (26 - 3)^{2}

使用根式运算法则:

n a^{n} = a

(26 - 3)^{2} = 26 - 3

= 26 - 3

e x p an d Δ x (x + Δ x^{2}) + x^{2}

e x p an d l im x \Rightarrow 2 (2 (x + 2) 2 - x)

e x p an d (- y^{'} (t) + 1)^{2}

e x p an d 4 f^{'} (- 1) (3 x + 4)

e x p an d \frac{e ^{2 x} ( 2 x + 1 )}{( x + 1 ) ^{2}}