Question

доведіть тотожність (4a+b)^2/16a^2+b^2+(4a-b)^2/b^2+16a^2=2

Answer 1

$\frac{(4a+b)^2}{16a^2+b^2}+\frac{(4a-b)^2}{b^2+16a^2}=\frac{(4a+b)^2+(4a-b)^2}{b^2+16a^2}=$

$\frac{16a^2+8ab+b^2+16a^2-8ab+b^2}{b^2+16a^2}=\frac{32a^2+2b^2}{16a^2+b^2}=\frac{2(16a^2+b^2)}{16a^2+b^2}=2$