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Question

Find the roots of the following equation 1x+4-1x-7=1130.


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Solution

Step 1: Estimate the value of a,b and c

Given equation is

1x+4-1x-7=1130

x-7-x-4x+4x-7=1130

-11x2-7x+4x-28=1130

x2-3x-28=-30

x2-3x+2=0

According to the Sridharacharya formula, for a given equation ax2+bx+c, the roots of this equation are given by

x=-b±b2-4ac2a

From the given equation we have,

a=1,b=-3,c=2

Step 2: Determine the roots of the equation

The roots of the equation are,

x=--3±-32-4×1×22×1

=3±9-82

=3±12

=42,22

=2,1

Hence, the roots of the equation are 2 and 1.


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