Question

If (4x+2y)^2=64 and xy=2 , what is the value of 4x^2+y^2?

Answer 1

8

Answer 2

\[(4x+2y)^2=64\]
\[xy=2\]
from the first equation, taking 2 out of the bracket, we get
\[4(2x+y)^2=64\]
dividing both sides by 4
\[(2x+y)^2=16\]
now
expanding the bracket, we get
\[4x^2+y^2+4xy=16\]
xy=2
so
\[4x^2+y^2+8=16\]
subtracting both sides by 8, we get
\[4x^2+y^2=8\]