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ohhh... I never thought I could post my homeworks here.. hmmm what can I ask, I'm having difficulty with my Calculus.. ^_^
Hello,
Thanks all of you for helping me,
again thanks
Annez I guess has done it the correct way..
4a²+b² If 2a+b =3 and ab=1
(2a+b)² =4a²+b²+4ab
4a²+b²=(2a+b) ² -4ab
=(3) ² -4x1
=9-4
=5
ANSWER = 5
ab=1 then a=1/b
then the equation 2a+b=3 gives 2/b+b=3 then 2+bsquare=3
3b-bsquare=2 then b(3-b)=2 and now u have 2 answers for b are b=2 and
3-b=2 then -b=2-3 b=1
if b=2 then ab=1 it gives a*2=1 then a=1/2
the equation 4a2+b2=(1/4)*1+(4)=17
if b=1 then ab=1 it gives a*1=1 then a=1
the equation 4a2+b2=(4*1)+1=5
hope it is helpfull for you.
The answer is 5:
Given: ab=1 a=1/b (eq. 1)
Given: 2a+b=3 and substituting for a from eq. 1:
2a+b=3 2/b+b=3 (eq. 2)
Multiply eq. 2 by b: b(2/b+b)=3b 2+b^2=3b or
b^2-3b+2=0 (eq. 3)
Factoring eq. 3 results in: (b-2)(b-1)=0
By the laws of multiplication, either b-2=0 or b-1=0
Therefore b=2 or b=1
If b=2: a(2)=1 so a=1/2 and 4a^2+b^2 = 4(1/2)^2*2^2 = 5
If b=1: a(1) = 1 so a=1 and 4a^2+b^2 = 4(1)^2*1^2 = 5
So do I get a prize for doing your homework?
4a²+b²= (2a+b)(2a+b)= 4a²+2ab+2ab+b²
now substitue and do the calculations!!!
answer is 9+2=11, I think