Question

How do i solve: 1/2(r+2)^2 = 1/3(2r-1)^2? The answer is supposed to be (-7+/-3√5)/2... how?

Answer 1

5r^2-14r-10=0 solve this one

Answer 2

it's 1.02255386... if I use the quadratic formula.

Answer 3

1,4+/-0,6*(11^0.5)

Answer 4

what? I'm so confused..

Answer 5

\[\frac12(r+2)^2=\frac13(2r-1)^2\]\[3(r+2)^2=2(2r-1)^2\]\[3(r^2+4r+4)=2(4r^2-4r+1)\]\[3r^2+12r+12=8r^2-8r+2\]\[5r^2-20r-10=0\]\[r^2-4r-2=0\]\[r=\frac{4\pm\sqrt{4^2-4(-2)}}{2}=2\pm\sqrt6\]...do I have the original problem right?

Answer 6

yes you did. Why is it 3(r+2)^2 = 2(2r-1)^2?

Answer 7

for the second step?

Answer 8

multiply both sides by 6

Answer 9

why by 6?

Answer 10

to get rid of the fractions and make life easier

Answer 11

(because 6 is the LCM of 2 and 3 if you want to think about it technically...)

Answer 12

ohh, okay. I get it now, thank you!

Answer 13

welcome, but it's not the answer you wanted...