tips to prove any number to any number directly

• Select the numbers which are to be proved equal to each other ex: 2 and 7
• Then write down the selected number multiples with negative sign
  

i.e -14 = -14

• Then write the numbers on both lhs and rhs in the form of square of selected number substracted by some number so that their results produce the numbers which are written above them i.e 4-18 = 49-63
• Then add square of a number on both sides which must be derived from dividing the substracting number by selected number and again by 2 i.e (-18)/(2)=-9 again divided by 2 gives -9/2 and similarly -63/7 = -9 again divided by 2 gives -9/2 note that the number obtained on both sides will be the same number.Then square the number and add it to both sides i.e 4-18+(81/4) = 49-63+(81/4)
• Then the present numbers will be of the form a2 + b2 -2ab which is equal to (a-b)2 next write down the numbers present in the above form i.e 22 + (9/2)2 - 2*2*(9/2) = 72 + (9/2)2 -2*7*(9/2)
  
• Then write them in their consized form like (2-(9/2))2 = (7-(9/2))2
  
• Take square root on both sides so we get (2-(9/2)) = (7-(9/2))
• Then move the calculated number from lhs to rhs so that the number gets cancled.Which produces the desired result i.e 2 = 7 -(9/2)+(9/2) => 2 = 7 .Hence proved