Question

So sánh:
a, \(25^{50}+3^{41}\) và \(2525^{25}+5^{31}\)
b, \(2^{30}+3^{30}+4^{30}+21^{12}\) và \(54^4+3.24^{10}\)

Answer 1

a) Ta có: \(25^{50}+3^{41}=\left(\left(25\right)^2\right)^{25}+\left(\left(3\right)^4\right)^{10}.3=625^{25}+81^{10}.3\)

\(2525^{25}+5^{31}=2525^{25}+\left(\left(5\right)^3\right)^{10}.5=2525^{25}+125^{10}.5\)

Vì \(625^{25}< 2525^{25}\),\(81^{10}.3< 125^{10}.5\)(\(81^{10}< 125^{10},3< 5\)) nên \(625^{25}+81^{10}.3< 2525^{25}+125^{10}.5\)

hay \(25^{50}+3^{41}< 2525^{25}+5^{31}\)

\(\)