Question

Пусть a+1/a=3 . Найдите a²+1/a²

Answer 1

A²+2*a*1/a+1/a²=9
a²+2+1/a²=9
a²+1/a²=7 

Answer 2

To find the value of a² + 1/a², we first need to square the equation a + 1/a = 3.

(a + 1/a)² = 3²

Expanding the left-hand side:

a² + 2(a)(1/a) + (1/a)² = 9

Since (a)(1/a) = 1 (the product of a number and its reciprocal is always 1):

a² + 2(1) + (1/a)² = 9

Now, we need to find the value of (1/a)². To do that, we'll square the equation a + 1/a = 3:

(a + 1/a)² = 3²

a² + 2(a)(1/a) + (1/a)² = 9

a² + 2 + (1/a)² = 9

Now, we can isolate (1/a)²:

(1/a)² = 9 - a² - 2

(1/a)² = 7 - a²

Now, we can find a² + 1/a²:

a² + 1/a² = a² + (7 - a²) = 7

So, the value of a² + 1/a² is 7.