Question

sqrt(5 x) - sqrt(5 x - 21) = 3

Answer 1

ehh x=5.

Answer 2

but for some reason when i try to solve it, i am unable to get the answer.

Answer 3

thats the right answer.. how do u do it? haha

Answer 4

what about this one: sqrt(2x - 10) + sqrt(x + 68) = 13

Answer 5

hmm inspection is enough to get the answer. but but i am doing something wrong while solving it.

Answer 6

x = 13

Answer 7

how are you getting these answers? are you asking someone else?

Answer 8

The way I would look at it, is to find an integer x such that 5x is a perfect square, and 5x-21 is a perfect square. Since 5x must be a perfect square, x must be divisible by 5. Also, 5x-21 must be greater than 0, so x is at least 5.

A natural guess would be to try 5 first. Fortunately, it works out.

Answer 9

what about the second equation I posted on here

Answer 10

how do u figure out if its perfect square or not?

Answer 11

For small numbers here, it's enough to just have a list of the first few perfect squares memorized

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, ... and so on. For now, just knowing the ones up to 100 would be good enough in most cases.

Answer 12

To solve the second equation, solving it by inspection/trial and error is just about the only way I've got also.