Question

If a + b = 4 and ab = 3 find 1 /square + 1 / a square?

Answer 1

Answer:

Required value of 1 / b^2 + 1 / a^2 is 10 / 9.

Step-by-step explanation:

= > ( a + b ) = 4

Square on both sides :

= > ( a + b )^2 = 4^2 = 16

= > a^2 + b^2 + 2ab = 16 { ( a + b )^2 = ( a + b )( a + b ) = a^2 + b^2 + 2ab }

= > a^2 + b^2 + 2( 3 ) = 16 { given, ab = 3 }

= > a^2 + b^2 = 16 - 6

= > a^2 + b^2 = 10

= > ( a^2 + b^2 ) / ( ab )^2 = 10 / ( ab )^2 { Dividing both sides by ( ab )^2 }

= > a^2 / ( ab )^2 + b^2 / ( ab )^2 = 10 / ( 3 )^2 { ( ab )^2 = 3^2 }

= > 1 / b^2 + 1 / a^2 = 10 / 9

Hence the required value of 1 / b^2 + 1 / a^2 is 10 / 9.