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प्रश्न
Using properties of proportion solve for x, given
`(sqrt(5x)+sqrt(2x -6))/(sqrt(5x)- sqrt(2x -6)) = 4`
उत्तर
`(sqrt(5x)+sqrt(2x -6))/(sqrt(5x)- sqrt(2x -6)) = 4/1`
Using componendo and dividendo on both sides
We know, if `a/b = c/d ⇒ (a+b)/(a- b)= ( c+ d) /( c- d) `
` ∴ ((sqrt(5x) + sqrt(2x -6)) + ( sqrt(5x) - sqrt(2x -6) ))/((sqrt(5x) + sqrt(2x - 6)) - (sqrt(5x) - sqrt(2x -6 ))) = (4+1)/(4-1)`
`sqrt(5x)/(sqrt(2x -6)) = 5/3`
On squaring both sides
`(5x)/(2x- 6) = 25/9`
45 x = 50x - 150
150 = 5x
`⇒ x = 150/5`
⇒ x = 30
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