If 9y^2 – 21y + 8 is rewritten as p^2 – 7p + 8, what is p in terms of y?

Answer 1

let p = 3y + a so the y^2 terms will cancel

then 9y^2 - 21y +8 = 9y^ 2+ 6ay + a^2 - 21y - 7a + 8

so a^2 + 6ay - 7a = 0

a(a + 6y - 7) = 0

a = 0 and a = 7 - 6y

so there are two solutions, p = 3y and p = 7 - 3y

Answer 2

Hi Alex,

I hope that you are doing well during this time, and that this message finds you in a good place.

To start these problems, you want to think of what you could replace "y" with to satisfy the expression.

1. 9y^2=p^2
2. -21y=-7p
3. -8=-8

Here the exponents are the same on both sides of the equal sign;

Solving 2nd equation we get 3y=p and put the value of p in equation 1st to check whether it satisfies or not.By putting value we can easily see that it does.

the only that you could replace y with, and satisfy the expression, is "p/3" and we will get the desired result

I hope that this helps. Feel free to reach out, if you need any more help!

Diksha