Anybody good at algebra?

I miss math so much I feel like doing your homework LOL. Let me think about it. Hmmm..

EDIT: So I wanted to use MS Math so I can template equations so it's easier to understand and that solve it a bit, but that thing freaking did it for me. So here it is. I'm going to leave the last 2 steps out since I don't want to spoon feed. The last number is up to you okay?

When did they add letters

Let's go through this step by step.

a = sqr (b) / k + 2

sqr (b) / k = a - 2

sqr (b) = k (a -2)

sqr (b) = ka - 2k

b = (ka - 2k) x (ka - 2k)

b = k²a² - 4k²a + 4k² (answer)

Check using a = 6 and k = 3

b = (3² x 6²) - (4 x 3² x 6) + (4 x 3²)

b = 324 - 216 + 36

b = 144

Substituting b = 144 into the first equation, a = sqr (b) / k + 2, we get

a = (sqr (144) / 3) + 2

a = (12 / 3) + 2

a = 4 + 2

a = 6

So the answer is

b = k²a² - 4k²a + 4k²

Not bad, considering that it is about 30yrs since I did any Algebra. Hopefully, this should help you with the rest of the questions if you approach them in a similar way. Don't forget to do the checking, substituting actual numbers, as shown above. You will need to work out for yourself suitable numbers to use at this step.

Nice Job Dwarf!!

Kirsch said:

Nice Job Dwarf!!

Thanks.

mickey megabyte said:

anybody good at washing up?

i've got a nice pile of dirty dishes growing in my kitchen..

I think I'll give that one a miss.

Dwarf said:

Let's go through this step by step.

a = sqr (b) / k + 2

sqr (b) / k = a - 2

sqr (b) = k (a -2)

sqr (b) = ka - 2k

b = (ka - 2k) x (ka - 2k)

b = k²a² - 4k²a + 4k² (answer)

Check using a = 6 and k = 3

b = (3² x 6²) - (4 x 3² x 6) + (4 x 3²)

b = 324 - 216 + 36

b = 144

Substituting b = 144 into the first equation, a = sqr (b) / k + 2, we get

a = (sqr (144) / 3) + 2

a = (12 / 3) + 2

a = 4 + 2

a = 6

So the answer is

b = k²a² - 4k²a + 4k²

Not bad, considering that it is about 30yrs since I did any Algebra. Hopefully, this should help you with the rest of the questions if you approach them in a similar way. Don't forget to do the checking, substituting actual numbers, as shown above. You will need to work out for yourself suitable numbers to use at this step.

Dwarf,
Nice job going step by step in solving his problem.
Could have done that early on in the post but thought it was important for the OP to practice and learn on his own. Isn't that the way we learned how to algebra?

I'm leaving the rest for him to work out on his own. Besides, the image isn't very clear with the other equations.