*Reciprocals*

This part deals with reciprocals. Using the method explained below many such problems can be solved merely by mental calculation alone.

Let us consider

x +1=10x 3

Under the usual method, we cross multiply to obtain a quadratic equation which is then solved to obtain 'x'.

But by *Vilokanam*
sutra of Vedic mathematics, the problem can be solved
merely at a glance by simple mental calculation.

10/3 can be written as 3 + 1/3 Therefore x +1= 3 +1x 3

==> x = 3 or 1/3

Similarly,

2) x +1=37= 6 +1x 6 6

Therefore from the sutra we have x = 6 or 1/6 3)1+x + 1=26= 5 +1x + 1 1 5 5

Therefore from the sutra we have x + 1 = 5 or 1/5 ==> x = 4 or -4/5 4)x - 3+x + 3=5= 2 +1x + 3 x - 3 2 2

Therefore we havex - 3= 2 or1x + 3 2 ==> x = -9 or 9 5) x +1=13x 6 Here 13/6 can be split up into 2/3 + 3/2 Therefore x +1=2+3x 3 2 ==> x = 2/3 or 3/2 6)x+x + 1=25=3+4x + 1 x 12 4 3 ==>x=4or3x + 1 3 4 ==> x = -4 or 3 7) x -1=5=3-2x 6 2 3 Therefore x = 3/2 or -2/3 8)x-x + 2=15=8-7x + 2 x 56 7 8 ==>x=8or -7x + 2 7 2 ==> x = -16 or -14/9