Question

A^4 + 1/a^2 при а + 1/а = 3

Answer 1

Ответ:      47 .

Пошаговое объяснение:

Значення  a⁴ + 1/a⁴ при а + 1/а = 3    ?

( а + 1/а )² = 3² ;

а² + 2а *1/а + ( 1/а )² = 9 ;

а² + 1/а² + 2 = 9 ;

а² + 1/а² = 7 ;

( а² + 1/а² )² = 7² ;

а⁴ + 2а² * 1/а² + 1/а⁴ = 49 ;

а⁴ + 1/а⁴ + 2 = 49 ;

 а⁴ + 1/а⁴ = 47 .

Answer 2

To solve this problem, we can substitute the value of "a + 1/a" into the expression and simplify it.

Given: a + 1/a = 3

We need to find the value of A^4 + 1/a^2.

Let's square the given equation (a + 1/a)^2 = 3^2:

(a + 1/a)^2 = 9 a^2 + 2 + 1/a^2 = 9 a^2 + 1/a^2 = 9 - 2 a^2 + 1/a^2 = 7

Now, let's find the value of A^4 + 1/a^2 by substituting the above value:

A^4 + 1/a^2 = (a^2)^2 + 1/a^2 = (a^2 + 1/a^2)^2 - 2 = (7)^2 - 2 = 49 - 2 = 47

Therefore, A^4 + 1/a^2 = 47 when a + 1/a = 3.