AIBU to ask for help with this maths question?

[whippetwoman]

Is anyone able to solve this practice SATS maths question?

16 + ?2 (that means something squared) = ?2 (something squared) - 4 x ?
Use three different cards to make this calculation correct: 6 12 10 8 25

Here is a picture version! It's number 4...

All help very much appreciated!

16 plus 6 squared = 10 squared minus 4 x 12
(Both are 52)

16 + x2 = y2 - 4z

6, 8, 10, 12, 25

52 = 100 - 48

So 6, 10 and 12.

I love you people! Thank you so much

See attached

Maths teachers - how do you teach children to approach this sort of question? Is it just an exercise in brute combinatorial working through the possibilities (bung each number in one at a time and see which works) or is there some strategy which speeds up the process?

I've been trying to think of an algorithm which would enable me to do this quickly, and I can't think of one.

16 + 6 (squared) = 10 ( squared) - 4 x 12 x because: 6 squared = 36
16+ 36= 52

10 squared = 100
4 x 12 = 48
100 - 48 = 52

Sorry didn't realise people had already explained

I usually ( and I do English not maths so not very efficient) just write a list of possibles - so what are all the square roots of the numbers, all of those plus 16, all of the possible multiplications by four and then see whats possible.

Edge - that's kind of what I meant by "brute combinatorics". I'm a theoretical physicist (aka applied applied mathematician) by trade, and this seems to me to be a question which tests the pupil's ability to carry out very boring arithmetic repeatedly, rather than a question which tests their mathematical ability, hence I'm wondering whether there's some hidden mathematical depths to it which I'm missing.

I suppose logically you can't square the 25 because then one side would be odd and one even.

Yes it's just trial and error improvement

I love homework questions posed on MN.

I like it more when people disagree though! There have been some howlers!

I did the 'trial & error' method too, though I'm sure there must be a better way. However, I ruled 25 out immediately, which saved time & effort!