There is an easy way to get it without guessing or squaring though. Multiply both sides by the difference of the square roots. The left side becomes x-(x-9)=9. Divide both sides by 9 to get that the difference of the 2 square roots is 1. Add this to the original equation and divide both sides by 2 to get the square root of x is equal to 5.
This is because the left side is positive (T), but you cannot conclude that the right side is positive. For example: (-3)^2 = 3^2 (True), but -3 = 3 (False)
√x + √(x-9) = 9
√x + √(x-9) = 5 + 4
=> √x = 5 => x=25
Check:
√25 + √(25-9)
= √25 + √(16)
= 5 + 4
= 9
you just guessed
There is an easy way to get it without guessing or squaring though. Multiply both sides by the difference of the square roots. The left side becomes x-(x-9)=9. Divide both sides by 9 to get that the difference of the 2 square roots is 1. Add this to the original equation and divide both sides by 2 to get the square root of x is equal to 5.
I think there is mistake although I has the same result 2:49
Because you have to set 45 - x >= 0 => x
This is because the left side is positive (T), but you cannot conclude that the right side is positive. For example: (-3)^2 = 3^2 (True), but -3 = 3 (False)