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rjkz [21]
3 years ago
10

(AM GIVING BRAINLIEST) Find all values of x such that x/(x - 5) =4/(x - 4)

Mathematics
2 answers:
Irina18 [472]3 years ago
4 0

Answer:

x = imaginary number

x₁ = 2<em>i</em>

x₂ = 6<em>i</em>

Step-by-step explanation:

x/(x - 5) =4/(x - 4)

x(x-4) = 4(x-5)

x*x + x*-4 = 4*x * 4*-5

x² -4x = 4x - 20

x² -4x - 4x + 20 = 0

x² - 8x + 20 = 0

x = {-(-8)±√((-8²)-(4*1*20))} / (2*1)

x = {8±√(64-80)} / 2

x = {8±√-16} / 2

√(-16) ∈<em> i</em>

<em>i </em>=  set of imaginary numbers

√-16 = -4<em>i</em>

then:

x = {8±(-4<em>i</em>) } / 2

x₁ = {8+(-4i)}/2 = {8-4i)/2 = 4i/2 = 2i

x₂ = {8-(-4)}/2 = {8+4i}/2 = 12i/2 = 6i

lesya [120]3 years ago
3 0

Answer:

\boxed{\sf x = 4 \pm 2i}

Step-by-step explanation:

\sf Solve  \: for  \: x: \\  \sf \implies \frac{x}{x - 5}  =  \frac{4}{x - 4}  \\  \\  \sf Cross \:  multiply: \\  \sf \implies x(x - 4) = 4(x - 5) \\  \\ \sf Expand  \: out  \: terms \:  of  \: the  \: left \:  hand \:  side: \\  \sf \implies {x}^{2}  - 4x = 4(x - 5) \\  \\  \sf Expand  \: out  \: terms \:  of \:  the \:  right \:  hand  \: side: \\  \sf \implies {x}^{2}  - 4x =  4x  - 20 \\  \\  \sf Subtract \:  4 x   \:  from  \: both  \: sides:\\  \sf \implies {x}^{2}  - 4x  - 4x =  4x  - 20  - 4x  \\ \\   \sf \implies {x}^{2}  - 8x  = - 20\\  \\  \sf Add  \: 16  \: to \:  both \:  sides: \\  \sf \implies {x}^{2}  - 8x + 16  = - 20 + 16 \\  \\  \sf\implies {x}^{2}  - 8x + 16  = -4 \\  \\  \sf Write  \: the \:  left  \: hand \:  side \:  as  \: a  \: square:  \\  \sf\implies {x}^{2}  - 4x - 4x + 16  = -4  \\   \\  \sf\implies x(x - 4)  - 4(x - 4)  = -4  \\   \\  \sf\implies (x - 4)(x - 4) = -4  \\  \\ \sf\implies {(x - 4)}^{2} =  - 4 \\  \\  \sf  Take  \: the  \: square \:  root  \: of \:  both  \: sides: \\  \sf\implies  \sqrt{ {(x - 4)}^{2}} =   \sqrt{ - 4}  \\  \\  \sf\implies x - 4 =  \pm 2i \\  \\  \sf Add \:  4  \: to  \: both \:  sides: \\  \sf\implies x - 4  + 4=  \pm 2i  + 4 \\   \\  \sf\implies x  =  4\pm 2i

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