Question

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Answer 1

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Answer 2

Given 3x + 2/x = 7 
squaring both the sides 

9x^2 + 4/x^2 + 12 = 49 ( as ( a+ b )^2 = a^2 + b^2 + 2ab ) 
9x^2 + 4/x^2 = 37
we know that 

( a - b )^2 = a^2 + b^2 - 2ab 
( a - b )^2 = a^2 + b^2 - 2ab + 2ab - 2ab ( adding and subtracting 2ab ) 
( a - b )^2 = ( a + b )^2 - 4ab 

Thus replacing a and b with 9x^2 and 4/x^2 respectively we get , 

( 9x^2 - 4/x^2 )^2 = ( 9x^2 + 4/x^2 )^2 - (4) (9x^2 ) ( 4/x^2 ) 
( 9x^2 - 4/x^2 )^2 = (37)^2 - (16)(9) 
( 9x^2 - 4/x^2 )^2 = 1369 - 144 
( 9x^2 - 4/x^2 )^2 = 1225 

9x^2 - 4/x^2 = √1225 
Hence 9x^2 - 4/x^2 = 35

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