Question

Дано а+1/а=3 вычислить а^2+1/a^2

Answer 1

а+1/а=3  Возведем в квадрат   (а+1/а)^2=9 Раскрываем скобки а^2+2+1/a^2=9  а^2+1/a^2=9-2   а^2+1/a^2=7

Answer 2

To find the value of а^2 + 1/а^2, we first need to manipulate the given equation а + 1/а = 3 to obtain а^2 + 1/а^2.

Step 1: Square the equation а + 1/а = 3 to get а^2 + 2а * (1/а) + 1/а^2 = 9.

Step 2: Simplify the middle term 2а * (1/а) = 2.

Step 3: Substitute the value of а^2 + 1/а^2 in the equation from step 1.

а^2 + 2 + 1/а^2 = 9.

Step 4: Now, isolate а^2 + 1/а^2 by subtracting 2 from both sides of the equation.

а^2 + 1/а^2 = 9 - 2.

а^2 + 1/а^2 = 7.

So, а^2 + 1/а^2 = 7.