Question

Giải phương trình 

36/x + 36/x-12 = 9/2

Answer 1

\(\frac{36}{x}+\frac{36}{x-12}=\frac{9}{2}\)

ĐKXĐ : x ≠ 0 ; x ≠ 12

pt ⇔ \(36\left(\frac{1}{x}+\frac{1}{x-12}\right)=\frac{9}{2}\)

⇔ \(\frac{x-12}{x\left(x-12\right)}+\frac{x}{x\left(x-12\right)}=\frac{1}{8}\)

⇔ \(\frac{x-12+x}{x\left(x-12\right)}=\frac{1}{8}\)

⇔ \(\frac{2x-12}{x\left(x-12\right)}=\frac{1}{8}\)

⇔ ( 2x - 12 ).8 = x( x - 12 )

⇔ 16x - 96 = x² - 12x

⇔ x² - 12x - 16x + 96 = 0

⇔ x² - 28x + 96 = 0 (1)

Δ' = b'² - ac = ( b/2 )² - ac = ( -14 )² - 96 = 100

Δ' > 0 nên (1) có hai nghiệm phân biệt

\(x_1=\frac{-b+\sqrt{\text{Δ}'}}{a}=\frac{14+\sqrt{100}}{1}=24\)(tm)

\(x_2=\frac{-b-\sqrt{\text{Δ}'}}{a}=\frac{14-\sqrt{100}}{1}=4\)(2)

Vậy phương trình có hai nghiệm x₁ = 24 ; x₂ = 4

Answer 2

\(\frac{36}{x}+\frac{36}{x-12}=\frac{9}{2}\)ĐKXĐ : \(x\ne0;12\)

\(\Leftrightarrow\frac{72\left(x-12\right)}{2x\left(x-12\right)}+\frac{72x}{2x\left(x-12\right)}=\frac{9x\left(x-12\right)}{2x\left(x-12\right)}\)

Khử mẫu : \(72\left(x-12\right)+72x=9x\left(x-12\right)\)

\(\Leftrightarrow72x-864+72x=9x^2-108x\)

\(\Leftrightarrow252x-864-9x^2=0\)

\(\Leftrightarrow9\left(x-24\right)\left(x-4\right)=0\Leftrightarrow x=24;4\)