sqrtx div sqrt(1-x)+sqrt(1-x)=5÷2
rArr sqrtx/sqrt(1 - x) + sqrt (1 - x) = 5/2
Taking L.C.M
rArr (sqrtx + 1 - x)/sqrt(1 - x) = 5/2
Cross Multiply
rArr 2 (sqrtx + 1 - x) = 5 sqrt(1 - x)
rArr 2sqrtx + 2 - 2x = 5 sqrt(1 - x)
Collect Like Terms
rArr 2sqrtx - 5 sqrt(1 - x) = 2x + 2
Square both sides
rArr (2sqrtx - 5 sqrt(1 - x))^2 = (2x + 2)^2
rArr (2sqrtx - 5 sqrt(1 - x)) (2sqrtx - 5 sqrt(1 - x)) = (2x + 2) (2x + 2)
rArr 4(x) - 20sqrt(1 - x) + 25(1 - x) = 4x^2 + 8x + 4
rArr 4(x) - 20sqrt(1 - x) + 25 - 25x = 4x^2 + 8x + 4
rArr- 20sqrt(1 - x) + 25 - 21x = 4x^2 + 8x + 4
rArr- 20sqrt(1 - x) = 4x^2 + 8x + 4 +21x - 25
rArr- 20sqrt(1 - x) = 4x^2 + 29x - 21
Square both sides
rArr (- 20sqrt(1 - x))^2 = (4x^2 + 29x - 21)^2
rArr 400 (1 - x) = (4x^2 + 29x - 21)^2
rArr 400 - 400x = (4x^2 + 29x - 21) (4x^2 + 29x - 21)
rArr 400 - 400x = 16x^4 + 232x^3 + 673x^2 - 1218x + 441
Collect like terms
rArr 16x^4 + 232x^3 + 673x^2 - 1218x + 400x + 441 - 400 = 0
rArr 16x^4 + 232x^3 + 673x^2 - 818x + 41 = 0
Solve the polynomial above..
That's how far i could get, But in my own point of view, i strongly doubt the Authenticity of the question..