展开 (1/x+1/y = 1/14)xy

解答

展开

(\frac{1}{x} + \frac{1}{y} = \frac{1}{14}) x y

y + x = 0.07142 \dots

求解步骤

(\frac{1}{x} + \frac{1}{y} = \frac{1}{14}) x y

= x (\frac{1}{x} + \frac{1}{14} = \frac{1}{y}) y

使用分配律:

a (b + c) = ab + a c

a = x y, b = \frac{1}{x}, c = \frac{1}{y} = \frac{1}{14}

x y \frac{1}{x} + x y \frac{1}{y} = \frac{1}{14}

\frac{1}{x} x y + \frac{1}{y} x y = \frac{1}{14}

化简

\frac{1}{x} x y + \frac{1}{y} x y = \frac{1}{14} : y + x = 0.07142 \dots

y + x = 0.07142 \dots

e x p an d (1 + sin (θ) + cos (θ))^{2}

s im pl i f y (2 + 1 + x)^{2}

e x p an d (x^{2} + 3 x + 2) (5 x + 9 x^{2} - 2 x)

s im pl i f y (\frac{1}{x} - 1) (\frac{1}{x} + 1)

e x p an d (4 - 4 cos (θ))^{2}