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put this solution on YOUR website!these sorts of questions are good standard maths questions, primarily because they see if you can convert English into Maths...remember 2 unknowns means you need (at least) 2 equations and the question is always written such that 2 equations can be produced. Also, these 2 particular questions are good in that they employ some -ve answers which some students will overlook.
1. Let the 2 intergers be x and y, so we know y-x=1 by definition!
Also, given is that (x+y)^2 = 49. So taking square roots, gives x+y=+7 but ALSO x+y=-7. Ignore the negative for now, just concentrate on the +ve..
Substitute into eqn2 the y=x+1 eqn gives x+x+1=7, so 2x=6 hence x=3. Therefore, y=4.
Now remember the -ve version too...that gives x=-4 and y=-3. Satisfy yourself that these also give 49.
2. Again, define two numbers x and y. We know that y=x+11 and that xy=-24. Second equation becomes x(x+11)=-24 by substituting the first equation. Multiply the bracket out and take the -24 to the other side gives x^2+11x+24=0.
This is factorised to (x+3)(x+8)=0. Hence x=-3 or x=-8. Therefore, y is found to be +8 or +3 respectively. Both sets of answers give the desired answer.
Jon.
