Question

If a2-3a+1=0 and a is not equal to 0. Find a+I upon a
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Answer 1

Answer:

3

Step-by-step explanation:

⇒ a² - 3a + 1 = 0

⇒ a² + 1 = 3a

     Divide both sides by a:

⇒ (a² + 1)/a = 3a

⇒ (a²/a) + (1/a) = 3a/a

⇒ a + (1/a) = 3

   Hence, the value of a + 1/a is 3

 Method 2:  if you're familiar with roots. Let the roots be x and y.

Product of roots = xy = 1  ⇒ y = 1/x

Sum of roots = x + y = - (-3) = 3

 Thus,

⇒ x + y = 3       ⇒ x + 1/x = 3

Replacing x with a(as x represents a):

⇒ a + 1/a = 3         required value

Answer 2

a²-3a+1 = 0 αnd α is not equal to 0

• a²+ 1 = 3a
• a² + 1 / a = 3 a
• a²/a + 1 / a = 3 a/a
• a + 1 / a = 3

So, a+1/a = 3

a+1/a = 3

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hope it helps