Question

Bài 1. Rút gọn

S= \(\sqrt{\frac{1}{a^2+b^2}+\frac{1}{\left(a+b\right)^2}+\sqrt{\frac{1}{a^4}+\frac{1}{b^4}+\frac{1}{\left(a^2+b^2\right)^2}}}\)

Answer 1

xét \(\sqrt{\frac{1}{a^4}+\frac{1}{b^4}+\frac{1}{\left(a^2+b^2\right)^2}}=\sqrt{\frac{b^4\left(a^2+b^2\right)^2+a^4\left(a^2+b^2\right)^2+a^4b^4}{a^4b^4\left(a^2+b^2\right)^2}}=\sqrt{\frac{a^8+b^8+2a^2b^6+a^4b^4+a^4b^4+2a^6b^2+a^4b^4}{\left[a^2b^2\left(a^2+b^2\right)\right]^2}}\)=\(\sqrt{\frac{\left(a^4+b^4\right)^2+2a^2b^2\left(a^4+b^4\right)+a^4b^4}{\left[a^2b^2\left(a^2+b^2\right)\right]^2}}=\sqrt{\frac{\left(a^4+b^4+a^2b^2\right)^2}{\left[a^2b^2\left(a^2+b^2\right)\right]^2}}\)