# Using Properties of Proportion Solve for X, Given √ 5 X + √ 2 X − 6 √ 5 X − √ 2 X − 6 = 4 - Mathematics

Sum

Using properties of proportion solve for x, given

(sqrt(5x)+sqrt(2x -6))/(sqrt(5x)- sqrt(2x -6)) = 4

#### Solution

(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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