Question

cho a+b=10 và ab=4. Hãy tính: a) A=a²+b²       b) B=a⁴+b⁴

 

Answer 1

a) vì a+b=10

=> \(\left(a+b\right)^2=10^2=100\)

\(< =>a^2+2ab+b^2=100\)

\(< =>a^2+b^2+2.4=100\)(vì ab=4)

\(< =>a^2+b^2=100-8\)

\(< =>a^2+b^2=92\)

b) theo câu a ta có \(a^2+b^2=92\)

\(< =>\left(a^2+b^2\right)^2=92^2=8464\)

\(< =a^4+b^4+2a^2b^2=8464\)

\(< =>a^4+b^4+2.\left(ab\right)^2=8464\)

\(< =>a^4+b^4+2.4^2=8464\)

\(< =>a^4+b^4=8464-32\)

\(< =>a^4+b^4=8432\)