i) Solve the following equation if x >= 0 ((5x + 2) ^ 2 + (5x – 2) ^ 2)/((5x + 2) ^ 2 – (5x – 2) ^ 2) = 13/12​

1 thought on “i) Solve the following equation if x >= 0 ((5x + 2) ^ 2 + (5x – 2) ^ 2)/((5x + 2) ^ 2 – (5x – 2) ^ 2) = 13/12​”

1. Answer:

   Correct option is

   A

   0.6

   Given

   (5x+2)

   2

   −(5x−2)

   2

   (5x+2)

   2

   +(5x−2)

   2

   =

   12

   13

   Applying the formulae, (a+b)

   2

   +(a−b)

   2

   =2(a

   2

   +b

   2

   )

   and (a+b)

   2

   −(a−b)

   2

   =4ab where a=5x;b=2

   4×(5x)×2

   2((5x)

   2

   +2

   2

   )

   =

   12

   13

   20x

   25x

   2

   +4

   =

   12

   13

   On cross multiplying and simplifying,

   75x

   2

   −65x+12=0

   75x

   2

   −20x−45x+12=0

   5x(15x−4)−3(15x−4)=0

   (5x−3)(15x−4)=

   x={

   5

   3

   ,

   15

   4

   }={0.6,0.27}

   Hence, m=0.6

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