Question

Aratati ca numarul 5¹⁰¹ se poate scrie ca suma de doua numere naturale patrate perfecte​

Answer 1

Răspuns:

5¹⁰¹=5¹·5¹⁰⁰=(1+4)·5¹⁰⁰=1·5¹⁰⁰+4·5¹⁰⁰=(5²)⁵⁰+2²·(5²)⁵⁰=(5⁵⁰)²+(2·5⁵⁰)²

Answer 2

Răspuns: Ai demonstrația mai jos

$\bf 5^{101} =5\cdot 5^{100} =$  

$\bf \big(1+4\big)\cdot5^{100} =$

$\bf \big(1^2+2^2\big)\cdot\big(5^{50}\big)^2 =$

$\bf \big(1\cdot5^{50}\big)^2 + \big(2\cdot5^{50}\big)^2 =$

$\red{\boxed{~\bf \Big(5^{50}\Big)^2 + \Big(2\cdot5^{50}\Big)^2~}}$