Question

Sa se afle numarul natural n stiind ca 7^n+7^n+1+5^n+2=399

Answer 1

 

7^n+7^n+1+5^n+2=399

Consider ca ecuatia trebuia scrisa asa:

7^(n) + 7^(n+1) + 7^(n+2) = 399

Rezolvare:

.

$\displaystyle\bf\\7^{n} + 7^{n+1} + 7^{n+2} = 399\\\\Dam~factor~comun~pe~7^n.\\\\7^n\Big(7^0+7^1+7^2\Big)=399\\\\7^n\Big(1+7+49\Big)=399\\\\57\times7^n=399\\\\7^n=\frac{399}{57}\\\\7^n=7\\\\7^n=7^1\\\\\implies~\boxed{\bf n=1}$

 

Answer 2

Cerința:

7ⁿ+7ⁿ+1+5ⁿ+2=399

Răspuns:

7ⁿ+7ⁿ+¹+7ⁿ+²=399

7ⁿ(7⁰+7¹+7²)=399

7ⁿ(1+7+49)=399

57•7ⁿ=399

7ⁿ=399/7 (399 supra 7)

7ⁿ=7

7ⁿ+7¹=> n=1