Question

√x+3+√x-3/√x+2-√x-3=5
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Answer 1

Answer:

$\frac{ \sqrt{x} + 3 + \sqrt{x} - 3 }{ \sqrt{x} + 2 - \sqrt{x} - 3 } = 5 \\ \frac{2 \sqrt{x} }{ - 1} = 5 \\ 2 \sqrt{x} = 5 \times ( - 1) \\ 2 \sqrt{x} = - 5 \\ \sqrt{x} = \frac{ - 5}{2} \\ x = \sqrt{ \frac{ - 5}{2} }$

Answer 2

Given : (√x+3+√x-3)/(√x+2-√x-3)=5

To Find : Solve for x

Solution:

(√(x+3)+√(x-3))/(√(x+2)-√(x-3))=5

cross multiply

=> √(x+3)+√(x-3) = 5(√(x+2)-√(x-3))

=> √(x+3)+√(x-3) = 5√(x+2)-5√(x-3)

=> √(x+3) + 6√(x-3) = 5√(x+2)

Squaring both sides

=> x + 3 + 36(x - 3) + 12√(x² - 9)  = 25(x + 2)

=>  37x - 105 +  12√(x² - 9)  = 25x + 50

=> 12x - 155  = -12√(x² - 9)

Squaring both sides

144x² + 155² - 3720x  = 144(x² - 9)

=> 144x² + 155² - 3720x  = 144 x² -  1296

=> 3720x =  155² + 1296

=> x = 25321/3720

=> x  = 6.8067

Learn More:

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