Identities - Finding Unlnown Coefficients
Having a bit of trouble with this one. Can anyone help?
Many thanks.
Q. Find the values of a & b if $\displaystyle (2x+a)^2 = 4x^2+12x+b$, for all x.
Attempt: $\displaystyle 4x^2+4xa+a^2 = 4x^2+12x+b$
$\displaystyle 4a = 12 => a = 3$
$\displaystyle a^2 = b => 3^2 = b => b = 9$
Ans. (From text book): a = 3, b = 7
Re: Identities - Finding Unlnown Coefficients
Quote:
Originally Posted by
GrigOrig99 
Q. Find the values of a & b if $\displaystyle (2x+a)^2 = 4x^2+12x+b$, for all x.
Attempt: $\displaystyle 4x^2+4xa+a^2 = 4x^2+12x+b$
$\displaystyle 4a = 12 => a = 3$
$\displaystyle a^2 = b => 3^2 = b => b = 9$
Ans. (From text book): a = 3, b = 7
The answer from the text is clearly wrong.
Say $\displaystyle x=1$ then $\displaystyle (2(1)+3)^2=25$ but $\displaystyle 4(1)^2+12(1)+7=23.$
