Question

33. If a + b = 4 and ab = 3; find 1/a² + 1/b²
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Answer 1

Step-by-step explanation:

= 1/a^2 + 1/b^2

= (1/a)^2 + (1/b)^2

= (1/a + 1/b)^2

= ((a + b/ab)^2 + 2 x 1/a x 1/b)

= ((4/3)^2 + 2/3)

= (16/9 + 2/3)

= (22/3)

therefore, 1/a^2 + 1/b^2 = 22/3

Answer 2

Answer:

10/9

Step-by-step explanation:

given that ,

a + b = 4

a = 4 - b ......(1)

also, given that

ab = 3 .....(2)

now putting the value of a from (1) on (2)

ab = 3

(4 - b)b = 3

4b - b² = 3

-b² + 4b - 3 = 0

-(b² - 4b + 3) = 0

b² - 4b + 3 = 0

b² - b - 3b + 3 = 0

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

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

now,

b - 3 = 0

b = 3

------------

b - 1 = 0

b = 1

now,

if b = 3

putting value of b = 3 on (1)

a = 4 - b

a = 4 - 3

a = 1

---------

if b = 1

putting value of b = 1 on (1)

a = 4 - b

a = 4 - 1

a = 3

to find 1/a² + 1/b²

putting the value of a and b

1/3² + 1/1²

1/9 + 1

= 10/9