Please solve these radical equations and show the steps so that I can understand them.
18-21, M
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ArishMell · 70-79, M
Having had half of SW puzzling over a set of unrelated expressions...
It's not easy doing maths on a plain text-editor either, because it does not allow you to type the indices etc properly.
(1) becomes 6x+9 = 81 (11-2 = 9 on RHS, then square both sides)
so 6x = 81-9
x = 12.
(2) That will become a regular quadratic equation if we re-arrange and square through.
sqrt(x-3) = x-3
x-3 = (x-3)^2.
I've a feeling I'm over-thinking this one. Though an equation so LHS=RHS, it is the sort that has a false air of symmetry to make you think you are missing something really obvious and simple, solvable mentally in two or three steps...!
x-3 = x^2-6x+9
I had to expand the expression by long-multiplication on paper as I could not remember how to do it mentally. It doesn't look right though. It seems too complicated, especially as the next step reveals a prime number in it:
x^2-7x = -12.
Or x^2-7x+12 = 0.
No. I'll have to admit defeat there I'm afraid. There is a rather long-winded formula for solving equations like that but I can't remember it, would struggle to find it and anyway I think I have gone completely wrong. Maths exercise questions tend to be designed to shake out quite neatly, like No.1 above, because it's practicing the technique that matters.
Oh well, fun trying......
It's not easy doing maths on a plain text-editor either, because it does not allow you to type the indices etc properly.
(1) becomes 6x+9 = 81 (11-2 = 9 on RHS, then square both sides)
so 6x = 81-9
x = 12.
(2) That will become a regular quadratic equation if we re-arrange and square through.
sqrt(x-3) = x-3
x-3 = (x-3)^2.
I've a feeling I'm over-thinking this one. Though an equation so LHS=RHS, it is the sort that has a false air of symmetry to make you think you are missing something really obvious and simple, solvable mentally in two or three steps...!
x-3 = x^2-6x+9
I had to expand the expression by long-multiplication on paper as I could not remember how to do it mentally. It doesn't look right though. It seems too complicated, especially as the next step reveals a prime number in it:
x^2-7x = -12.
Or x^2-7x+12 = 0.
No. I'll have to admit defeat there I'm afraid. There is a rather long-winded formula for solving equations like that but I can't remember it, would struggle to find it and anyway I think I have gone completely wrong. Maths exercise questions tend to be designed to shake out quite neatly, like No.1 above, because it's practicing the technique that matters.
Oh well, fun trying......