Question

If a + b = 4 and ab = 3; find 1/b²+1/a²​

Answer 1

Answer:

       10 / 9

Step-by-step explanation:

ab = 3 ------{i}

a + b = 4

a = 4 - b ------{ii}

from {i} and {ii}

b(4 - b) = 3

4b - b² = 3

b² - 4b + 3 = 0

b² - b - 3b + 3 = 0

b (b - 1) - 3 (b - 1) = 0

(b - 3) (b - 1) = 0

b = 1 , 3

ab = 3

Case 1  -  3a = 3                                 case 2  -  1a = 3

                 a = 1                                                    a = 3

∴ a = 3 , b = 1

          or

  b = 3 , a = 1

1/b² + 1/a²​

= a² + b² / a²b²

= (3)² + (1)² / 3² × 1²

= 9 + 1 / 9 × 1

= 10 / 9

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