What are the solutions for sqr. root of x minus the square root of x-20 equals 10?

Question

\/``x+\/``x-20=10

Answer 1

Not going to give you the answer, but I'll lead you down the path.

Move "10" to the left side of the equation and sqrt(x-20) to the right side, then "square" both sides of the equation, and you'll end up with just one sqrt to contend with. Move the numbers around a bit more, and another "square" of both sides of the equation and you got "x"

Answer 2

i think of : sqrt(x-20) = 10 - sqrt (x) squaring the two factors yields x-20 = a hundred -20 sqrt (x) +x combining and segregating 20 sqrt(x) = one hundred twenty sqrt (x) = 6 squaring the two factors yields x =36

Answer 3

sqrt(x) + sqrt(x-20) = 10
sqrt(x-20) = 10 - sqrt(x)

square both sides
x-20 = 100 - 20sqrt(x) + x
-20 = 100-20sqrt(x)
20sqrt(x) = 100+20 = 120
sqrt(x) = 6
x = 36.

sqrt(36) + sqrt(36-20) = 10
6 + sqrt(16) = 10
6 + 4 = 10

Answer 4

sqrt(x) - sqrt(x - 20) = 10
sqrt(x) = sqrt(x - 20) + 10
square both sides
x = (sqrt(x - 20) + 10)(sqrt(x - 20) + 10)
x = (x - 20) + 10sqrt(x - 20) + 10sqrt(x - 20) + 100
x = x - 20 + 20sqrt(x - 20) + 100
x = x + 20sqrt(x - 20) + 80

subtract "x" and 80 from both sides

20sqrt(x - 20) = -80
sqrt(x - 20) = -4

square both sides

x - 20 = 16
x = 36

ANS : 36

Answer 5

You said minus but your wrote plus. With minus the equation is false.

the answer is x=36

Answer 6

sqrtx - sqrt (x - 20) = 10
[sqrtx - sqrt (x - 20)]^2 = 100
x + x - 20 - 2sqrt(x^2 - 20x) = 100
2x - 20 - 100 = 2sqrt(x^2 - 20x)
2x - 120 = 2sqrt(x^2 - 20x)
x - 60 = sqrt(x^2 - 20x)
(x - 60)^2 = x^2 - 20x
x^2 - 120x + 3600 - x^2 + 20x = 0
x^2 - x^2 - 120x + 20x = -3600
-100x = -3600
x = 36
phew.